19 Results Found

In the present paper, we give a simple proof of the Chen–Ricci inequality for submanifolds in Riemannian and Lorentzian space forms, respectively. Moreover, we extend the Chen–Ricci inequality to submanifolds in Lorentzian manifolds with...

In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen–Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Additional...

We investigate f-biharmonic submanifolds in T-space form, where we analyze different scenarios and provide necessary and sufficient conditions for f-biharmonicity. We also derive a non-existence result for f-biharmonic submanifolds where $\xi$ and $$...

This article explores the Ricci tensor of slant submanifolds within locally metallic product space forms equipped with a semi-symmetric metric connection (SSMC). Our investigation includes the derivation of the Chen–Ricci inequality and an in-d...

This paper aims to develop a general theory of quaternion Kahlerian statistical manifolds and to study quaternion CR-statistical submanifolds in such ambient manifolds. It extends the existing theories of quaternion submanifolds and totally real subm...

The geometry of submanifolds in Kähler manifolds is an important research topic. In the present paper, we study submanifolds in complex space forms admitting a semi-symmetric non-metric connection. We prove the Chen–Ricci inequality, Chen...

This research examines key inequalities associated with the scalar and Ricci curvatures of slant submersions within generalized Sasakian space forms (GSSFs). We establish significant geometric constraints and conduct a detailed analysis of the condit...

In the present paper, we establish some basic inequalities involving the Ricci and scalar curvature of the vertical and the horizontal distributions for hemi-slant submersions having the total space a complex space form. We also discuss the equality...

We give a simple proof of the Chen inequality involving the Chen invariant $\delta (k)$ of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for stat...

We consider statistical submanifolds of Hessian manifolds of constant Hessian curvature. For such submanifolds we establish a Euler inequality and a Chen-Ricci inequality with respect to a sectional curvature of the ambient Hessian manifold.

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds wh...

The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated...

We establish Chen inequality for the invariant $\delta (2,2)$ on statistical submanifolds in Hessian manifolds of constant Hessian curvature. Recently, in co-operation with Chen, we proved a Chen first inequality for such submanifolds. The...

In this article, we derive Chen’s inequalities involving Chen’s $\delta$-invariant ${\delta }_M$, Riemannian invariant $\delta (m_1,\cdots ,m_k)$, Ricci curvature, Riemannian invariant ${\mathsf{\Theta }}_k(2\le k\le m)$, the scalar curvature and the squared of...

In this work, the cases of non-integrable distributions in a Riemannian manifold with the first generalized semi-symmetric non-metric connection and the second generalized semi-symmetric non-metric connection are discussed. We obtain the Gauss, Codaz...

In this paper, we focus on non-integrable distributions with a quarter-symmetric non-metric connection (QSNMC) in generalized Riemannian manifold. First, by studying a quarter-symmetric connection on the generalized Riemannian manifold, we obtain the...

This editorial presents 26 research articles published in the Special Issue entitled Differentiable Manifolds and Geometric Structures of the MDPI Mathematics journal, which covers a wide range of topics particularly from the geometry of (pseudo-)Rie...

In the present paper, we investigate the geometry and topology of warped product Legendrian submanifolds in Sasakian space forms ${\mathbb{D}}^{2n+1}\left(ϵ\right)$ and obtain the first Chen inequality that involves extrinsic invariants like the mean curvature and the length o...

Warped products play crucial roles in differential geometry, as well as in mathematical physics, especially in general relativity. In this article, first we define and study statistical solitons on Ricci-symmetric statistical warped products $\mathbb{R}{\&}_{}$...