Search Results (26)

Background: Due to the congested competition calendar and the high physical demands of elite basketball, the selection of effective recovery strategies is essential to optimize performance and reduce exercise-induced fatigue and muscle damage. This pilot study aimed to examine the acute effects of different nutritional and physical recovery strategies on exercise performance, muscle damage, and perceived fatigue and exertion in elite basketball players. Methods: Fifteen elite male basketball players participated in this pilot randomized crossover trial and completed four recovery conditions: cold-water immersion (CWI), active recovery (ACT), protein–carbohydrate supplementation (SUP), and placebo (PLA). Following a basketball-specific fatigue protocol, creatine kinase, countermovement jump performance, isometric strength, 10 m sprint, and 4 × 10 m shuttle run tests were assessed at baseline, immediately post-exercise, and 24 h post-exercise. Perceived fatigue and rate of perceived exertion were measured at baseline, immediately post-exercise, immediately after the recovery intervention, and 24 h post-exercise. Results: The three recovery methods attenuated the 24 h exercise-induced increase in CK compared with the placebo condition (p > 0.05). CWI, SUP and ACT decreased fatigue and RPE immediately after their application (p < 0.05), while PLA kept them elevated. CWI was associated with a significant improvement in 4 × 10 m SRT performance (p = 0.027). Conclusions: Nutritional supplementation and physical recovery strategies effectively attenuated exercise-induced muscle damage and fatigue in elite basketball players. However, CWI demonstrated the most pronounced acute benefits for physical performance recovery. Full article

Let $(M,g)$ be a connected, compact Riemannian manifold of dimensionan n. We demonstrate that, after a suitable normalization, a shrinking gradient Ricci soliton $(M,g,f,\lambda )$ is trivial exactly when the mean value of f is less than or equal to $\frac{n}{2}$. Moreover, we prove that a normalized non-steady gradient Ricci soliton $(M,g,f,\lambda )$ is trivial if and only if its scalar curvature S satisfies the relation $S=\lambda \left(f+\frac{n}{2}\right).$ In addition, we establish that if $(M,g,f,\lambda )$ admits an isometric immersion as a hypersurface in the Euclidean space, then the soliton must necessarily be of a shrinking type. In such a case, the constant $\lambda$ and the mean curvature of M satisfy a certain inequality, with equality occurring precisely when M is isometric to a round sphere. Full article

This paper presents a detailed investigation into the isometric properties of osculating and rectifying curves on smooth immersed surfaces in ${\mathbb{E}}^3$. We examine the geometric interactions between these curves, specifically when the osculating curve is associated with one surface and the rectifying curve with another. The main objective of this study is to identify the conditions under which these curves exhibit isometric behavior, preserving their intrinsic geometric properties along their respective Frenet frames. Our findings demonstrate that these curves retain isometric characteristics along the tangent, normal, and binormal directions, offering new insights into their structural invariance. This research makes a significant contribution to the broader field of differential geometry, with potential applications in surface theory. Full article

This paper investigates compact Riemannian hypersurfaces immersed in $(n+1)$-dimensional Riemannian or Lorentzian manifolds that admit concircular vector fields, also known as closed conformal vector fields (CCVFs). We focus on the support function of the hypersurface, which is defined as the component of the conformal vector field along the unit-normal vector field, and derive an expression for its Laplacian. Using this, we establish integral formulae for hypersurfaces admitting CCVFs. These results are then extended to compact Riemannian hypersurfaces isometrically immersed in Riemannian or Lorentzian manifolds with constant sectional curvatures, highlighting the crucial role of CCVFs in the study of hypersurfaces. We apply these results to provide characterizations of compact Riemannian hypersurfaces in Euclidean space ${\mathbb{R}}^{n+1}$, Euclidean sphere $S^{n+1}$, and de Sitter space $S_1^{n+1}$. Full article

Background/Objectives: The aim of this study was to assess the effects of cold-water immersion (CWI) post-eccentric muscle contraction exercise on skin temperature, pain score, maximum voluntary isometric contraction (MVIC), muscle damage, and muscle mechanical properties. Methods: Twenty-seven male participants (age 20.6 ± 0.6; body mass 69.4 ± 8.1; body fat % 13.7 ± 4.3) were divided into three treatments: whole-body CWI treatment group (n = 9), lower-body CWI treatment group (n = 9), and control treatment group (n = 9). Results: MVIC did not show a significant interaction effect between group and time but demonstrated a significant main effect for time (p = 0.001). The pain scale demonstrated a significant interaction effect between group and treatment (p = 0.049), in addition to significant main effects for both time and treatment (both p = 0.001). While blood creatine kinase (CK) concentration revealed no significant interaction effect between group and time, a significant main effect was observed for time (p = 0.001). Blood lactate dehydrogenase (LDH) concentration showed both a significant interaction effect between group and time (p = 0.02) and a significant main effect for time (p = 0.001). The tensiomyography (TMG) results for Dm showed a significant interaction effect between group and treatment (p = 0.047), as well as a significant main effect for time (p = 0.001). Conclusions: Lower-body CWI is effective in reducing pain indices and blood LDH levels, a marker of muscle damage. It may serve as an effective method for preventing and minimizing pain and muscle damage, comparable to whole-body CWI. Full article

(1) Background: The recovery method is important and decisive in the training system. This study aimed to assess the effects of various post-training recovery methods on muscle damage and strength indicators in Paralympic powerlifting athletes. (2) Methods: A crossover study was conducted involving eleven male athletes (25.4 ± 3.3 years, 70.3 ± 12.1 kg). Muscle damage was assessed using blood biochemical markers (cytokines IL-6, IL-10, and TNF-α) and isometric force indicators, including the maximum isometric force (MIF), time to MIF, and Rate of Force Development. The following assessments were performed before, immediately after, and at 24 and 48 h after the recovery protocol: (a) passive recovery (RP) or (b) cold-water immersion (CWI). (3) Results: The main results indicated that maximum isometric force (MIF) significantly improved after 48 h of CWI application (p < 0.05; for all comparison). The analysis of biochemical markers did not yield significant differences between the recovery methods at different time points (p > 0.05). For IL-6, there were significant differences between CWI before (2.29 ± 1.08, 95% CI 1.57–3.01) and CWI 2 h later (2 h) (4.59 ± 2.96, 95% CI 2.60–6.57; p = 0.045), and between CWI 15 min later (15 min) (4.14 ± 2.24, 95% CI 2.63–5.64) and CWI 48 h later (48 h) (2.33 ± 1.25, 95% CI 1.49–3.17; p = 0.034). There were differences between CWI 2 h (4.14 ± 2.24, 95% CI 2.63–5.64) and CWI 48 h later (2.33 ± 1.25, 95% CI 1.49–3.17; p = 0.035; F = 9.202; η²p = 0.479; high effect). (4) Conclusions: CWI significantly improved the post-resistance training muscle damage and strength in Paralympic powerlifting athletes. Full article

The main aim of this paper is to study some properties of submanifolds in a Riemannian manifold equipped with a new structure of golden type, called the ($\alpha , p$)-golden structure, which generalizes the almost golden structure (for $\alpha =1$) and the almost complex golden structure (for $\alpha =-1$). We present some characterizations of isometrically immersed submanifolds in an ($\alpha , p$)-golden Riemannian manifold, especially in the case of the semi-invariant submanifolds, and we find some conditions for the integrability of the distributions. Full article

This research aims to prove a sharp relationship between statistical submersions and doubly minimal immersions. We consider a non-trivial statistical submersion on a statistical manifold with isometric fibers. Then, we investigate that it cannot be isometrically immersed as a doubly minimal manifold into any statistical manifold of non-positive sectional curvature using a submersion invariant for dual connections and additional conditions. Full article

Background and objectives: The main problem of vascular preservation is the maintenance of vessel graft quality and function following extended storage. Conventional preservation solutions such as histidine–tryptophan–ketoglutarate (HTK) solution, Phosphate-Buffer Solution (PBS), or sodium chloride 0.9% has been shown to be inadequate in preserving vascular physiological function after 3 days of cold storage. This study aimed to evaluate whether adenosine and lidocaine (AL) in a modified Krebs–Henseleit (KH) solution can preserve the function and histological structure of rat aortic rings after 6 days. Materials and Methods: Thirty-five aortic rings from male Wistar rats (200–300 g) were harvested and immediately immersed in one of the assigned cold preservation solutions: standard KH, modified KH (mod KH) with lower calcium (Ca²⁺) and higher magnesium content (Mg²⁺) with or without adenosine and lidocaine (mod KH-AL), and modified KH with AL, insulin, and melatonin (Mod KH-ALMI). The contraction and relaxation function of the aortic rings were examined using an isometric force transducer after 6 days of cold preservation. Hematoxylin and eosin staining were used to analyze the rings’ histological structure. Results: Vascular contraction and relaxation functions were severely affected after a 6-day cold storage period in standard KH. Modifying the KH solution by reducing the Ca²⁺ and increasing the Mg²⁺ levels greatly recovered the vessel functions. The addition of AL or ALMI to the modified KH did not further recover vascular contractility. However, only the addition of AL to the modified KH increased the ACh-induced relaxation at 6 days when compared to the conventional KH, suggesting that endothelium preservation is improved. From histological analysis, it was found that the addition of AL but not ALMI further improved the endothelial lining and the structure of the elastic membrane layers of the preserved vessels after 6 days of cold preservation. Conclusions: The addition of AL to low calcium-high magnesium KH solution significantly enhanced endothelial preservation and improved endothelial-induced relaxation of preserved vessels after 6 days of cold storage. Full article

Cold water immersion (CWI) and percussive massage therapy (PMT) are commonly used recovery techniques in team sports. In particular, despite its wide use, PMT has been scarcely investigated in the literature, especially regarding neuromuscular measures and in comparison with other techniques. This study aimed to evaluate and compare the acute and short-term effects (24 h) of CWI and PMT on muscle strength, contractile properties, and soreness after exercise. A randomized crossover study was performed on sixteen male soccer players (22 years, 20–27) who participated in three experimental sessions involving a fatiguing protocol consisting of a Yo-Yo Intermittent Endurance Test followed by 3 × 10 squat jumps and a wall sit for 30 s, and 12 min of recovery including CWI (10 °C water), bilateral PMT on the anterior and posterior thigh, or passive resting. Outcomes were assessed immediately after the exercise protocol, after the recovery intervention, and at 24 h. Isometric knee extension (IKE) and flexion (IKF) and tensiomyography (TMG) were assessed. Muscle soreness and fatigue were scored from 0 to 10. PMT increased strength after the treatment (p = 0.004) and at 24 h (p = 0.007), whereas no significant differences were found for the other two recovery modalities. At post-recovery, compared to CON, CWI resulted in a longer TMG contraction time (p = 0.027). No significant differences were found at 24 h. Finally, PMT and CWI enhanced muscle soreness recovery compared to passive rest (F_4,60 = 3.095, p = 0.022, _pη² = 0.171). Preliminary results from this study suggest that PMT might improve isometric strength after strenuous exercise, and both PMT and CWI reduce muscle soreness perception, while the effects on TMG parameters remain controversial. Full article

f-biharmonic maps are generalizations of harmonic maps and biharmonic maps. In this paper, we give some descriptions of f-biharmonic curves in a space form. We also obtain a complete classification of proper f-biharmonic isometric immersions of a developable surface in ${\mathbb{R}}^3$ by proving that a proper f-biharmonic developable surface exists only in the case where the surface is a cylinder. Based on this, we show that a proper biharmonic conformal immersion of a developable surface into ${\mathbb{R}}^3$ exists only in the case when the surface is a cylinder. Riemannian submersions can be viewed as a dual notion of isometric immersions (i.e., submanifolds). We also study f-biharmonicity of Riemannian submersions from 3-manifolds by using the integrability data. Examples are given of proper f-biharmonic Riemannian submersions and f-biharmonic surfaces and curves. Full article

In this paper, we estimate Ricci curvature inequalities for a hemi-slant warped product submanifold immersed isometrically in a generalized complex space form with a nearly Kaehler structure, and the equality cases are also discussed. Moreover, we also gave the equivalent version of these inequalities. In a later study, we will exhibit the application of differential equations to the acquired results. In fact, we prove that the base manifold is isometric to Euclidean space under a specific condition. Full article

On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form $\theta$, we consider natural $ϵ$-contractions, i.e., contractions $g_{ϵ}^M$ of the Levi form $G_{\theta }$, such that the norm of the Reeb vector field T of $(M, \theta )$ is of order $O\left({ϵ}^{-1}\right)$. We study isopseudohermitian (i.e., $f^{\ast }\mathsf{\Theta }=\theta$) Cauchy–Riemann immersions $f:M\to (A,\mathsf{\Theta })$ between strictly pseudoconvex CR manifolds M and A, where $\mathsf{\Theta }$ is a contact form on A. For every contraction $g_{ϵ}^A$ of the Levi form $G_{\mathsf{\Theta }}$, we write the embedding equations for the immersion $f:M\to \left(A,g_{ϵ}^A\right)$. A pseudohermitan version of the Gauss equation for an isopseudohermitian C-R immersion is obtained by an elementary asymptotic analysis as $ϵ\to 0^{+}$. For every isopseudohermitian immersion $f:M\to S^{2N+1}$ into a sphere $S^{2N+1}\subset {\mathbb{C}}^{N+1}$, we show that Webster’s pseudohermitian scalar curvature R of $(M, \theta )$ satisfies the inequality $R\le 2n\left[\left(f^{\ast }{g}_{\mathsf{\Theta }}\right)(T,T)+n+1\right]+\frac{1}{2}\{\parallel H\left(f\right){\parallel }_{g_{\mathsf{\Theta }}^f}^2+\parallel {\mathrm{trace}}_{G_{\theta }}{\mathsf{\Pi }}_{H\left(M\right)}\left({\nabla }^{\top }-\nabla \right){\parallel }_{f^{\ast }{g}_{\mathsf{\Theta }}}^2\}$ with equality if and only if $B\left(f\right)=0$ and ${\nabla }^{\top }=\nabla$ on $H\left(M\right)\otimes H\left(M\right)$. This gives a pseudohermitian analog to a classical result by S-S. Chern on minimal isometric immersions into space forms. Full article

The article introduces invariants of a Riemannian manifold related to the mutual curvature of several pairwise orthogonal subspaces of a tangent bundle. In the case of one-dimensional subspaces, this curvature is equal to half the scalar curvature of the subspace spanned by them, and in the case of complementary subspaces, this is the mixed scalar curvature. We compared our invariants with Chen invariants and proved geometric inequalities with intermediate mean curvature squared for a Riemannian submanifold. This gives sufficient conditions for the absence of minimal isometric immersions of Riemannian manifolds in a Euclidean space. As applications, geometric inequalities were obtained for isometric immersions of sub-Riemannian manifolds and Riemannian manifolds equipped with mutually orthogonal distributions. Full article

This study aimed to investigate the effects of cold-water immersion (CWI) and sports massage on delayed-onset muscle soreness (DOMS) in amateur athletes. Sixty male amateur athletes were randomised into four equal groups (n = 15) receiving either CWI, sports massage, their combination, or served as controls after applying plyometric training to their lower extremities. The main outcomes measures were pain, exertion, rectus femoris perimeter, knee flexion range of motion, knee extensors isometric strength and serum creatine phosphokinase (CPK) levels examined before the plyometric training, immediately after the treatment, and 24, 48 and 72 h post exercise. We observed no significant differences between study groups in the most tested variables. CWI improved pain compared to the combined application of CWI and sports massage, and the control group both on the second and third day post exercise. Sports massage combined with CWI also led to a significant reduction in pain sensation compared to the control group. In conclusion the treatment interventions used were effective in reducing pain but were unable to affect other important adaptations of DOMS. Based on the above, sports scientists should reconsider the wide use of these interventions as a recovery strategy for athletes with DOMS. Full article