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Search Results (4)

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Keywords = gradient almost Yamabe solitons

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6 pages, 177 KiB  
Editorial
Differentiable Manifolds and Geometric Structures
by Adara M. Blaga
Mathematics 2025, 13(7), 1082; https://doi.org/10.3390/math13071082 - 26 Mar 2025
Viewed by 425
Abstract
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-)Riemannian manifolds and their submanifolds, providing some of the [...] Read more.
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-)Riemannian manifolds and their submanifolds, providing some of the latest achievements in different areas of differential geometry, among which is counted: the geometry of differentiable manifolds with curvature restrictions such as Golden space forms, Sasakian space forms; diffeological and affine connection spaces; Weingarten and Delaunay surfaces; Chen-type inequalities for submanifolds; statistical submersions; manifolds endowed with different geometric structures (Sasakian, weak nearly Sasakian, weak nearly cosymplectic, LP-Kenmotsu, paraquaternionic); solitons (almost Ricci solitons, almost Ricci–Bourguignon solitons, gradient r-almost Newton–Ricci–Yamabe solitons, statistical solitons, solitons with semi-symmetric connections); vector fields (projective, conformal, Killing, 2-Killing) [...] Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
14 pages, 305 KiB  
Article
Rigidity and Triviality of Gradient r-Almost Newton-Ricci-Yamabe Solitons
by Mohd Danish Siddiqi and Fatemah Mofarreh
Mathematics 2024, 12(20), 3173; https://doi.org/10.3390/math12203173 - 10 Oct 2024
Viewed by 809
Abstract
In this paper, we develop the concept of gradient r-Almost Newton-Ricci-Yamabe solitons (in brief, gradient r-ANRY solitons) immersed in a Riemannian manifold. We deduce the minimal and totally geodesic criteria for the hypersurface of a Riemannian manifold in terms of the [...] Read more.
In this paper, we develop the concept of gradient r-Almost Newton-Ricci-Yamabe solitons (in brief, gradient r-ANRY solitons) immersed in a Riemannian manifold. We deduce the minimal and totally geodesic criteria for the hypersurface of a Riemannian manifold in terms of the gradient r-ANRY soliton. We also exhibit a Schur-type inequality and discuss the triviality of the gradient r-ANRY soliton in the case of a compact manifold. Finally, we demonstrate the completeness and noncompactness of the r-Newton-Ricci-Yamabe soliton on the hypersurface of the Riemannian manifold. Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
12 pages, 274 KiB  
Article
h-Almost Ricci–Yamabe Solitons in Paracontact Geometry
by Uday Chand De, Mohammad Nazrul Islam Khan and Arpan Sardar
Mathematics 2022, 10(18), 3388; https://doi.org/10.3390/math10183388 - 18 Sep 2022
Cited by 6 | Viewed by 1880
Abstract
In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h [...] Read more.
In this article, we classify h-almost Ricci–Yamabe solitons in paracontact geometry. In particular, we characterize para-Kenmotsu manifolds satisfying h-almost Ricci–Yamabe solitons and 3-dimensional para-Kenmotsu manifolds obeying h-almost gradient Ricci–Yamabe solitons. Then, we classify para-Sasakian manifolds and para-cosymplectic manifolds admitting h-almost Ricci–Yamabe solitons and h-almost gradient Ricci–Yamabe solitons, respectively. Finally, we construct an example to illustrate our result. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
8 pages, 254 KiB  
Article
Characterization of Almost Yamabe Solitons and Gradient Almost Yamabe Solitons with Conformal Vector Fields
by Ali H. Alkhaldi, Pişcoran Laurian-Ioan, Abimbola Abolarinwa and Akram Ali
Symmetry 2021, 13(12), 2362; https://doi.org/10.3390/sym13122362 - 8 Dec 2021
Cited by 3 | Viewed by 2312
Abstract
In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields [...] Read more.
In this paper, some sufficient conditions of almost Yamabe solitons are established, such that the solitons are Yamabe metrics, by which we mean metrics of constant scalar curvature. This is achieved by imposing fewer topological constraints. The properties of the conformal vector fields are exploited for the purpose of establishing various necessary criteria on the soliton vector fields of gradient almost Yamabe solitons so as to obtain Yamabe metrics. Full article
(This article belongs to the Special Issue Recent Advance in Pure and Applied Mathematics)
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