Results 51 to 60 of about 207 (126)
A half-space type property in the Euclidean sphere [PDF]
, 2022 summary:We study the notion of strong $r$-stability for the context of closed hypersurfaces $\Sigma ^n$ ($n\ge 3$) with constant $(r+1)$-th mean curvature $H_{r+1}$ immersed into the Euclidean sphere $\mathbb{S}^{n+1}$, where $r\in \lbrace 1,\ldots ,n-2 ...
Velásquez, Marco Antonio Lázaro
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Multiplicative rectifying submanifolds of multiplicative Euclidean space
Mathematical Methods in the Applied Sciences, Volume 48, Issue 1, Page 329-339, 15 January 2025.In this paper, we initiate the study of the multiplicative Euclidean submanifolds, exhibiting the multiplicative counterparts of the Gauss–Weingarten formulas. Some particular types such as multiplicative conic, spherical, and totally geodesic submanifolds are analyzed.
Muhittin Evren Aydin +2 more
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Lightlike Hypersurfaces of Indefinite Generalized Sasakian Space Forms
Journal of Applied Mathematics, Volume 2015, Issue 1, 2015., 2015 We study lightlike hypersurfaces M of an indefinite generalized Sasakian space form M-(f1,f2,f3), with indefinite trans‐Sasakian structure of type (α, β), subject to the condition that the structure vector field of M- is tangent to M. First we study the general theory for lightlike hypersurfaces of indefinite trans‐Sasakian manifold of type (α, β ...
Dae Ho Jin, Dimitris Fotakis
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Constrained deformations of positive scalar curvature metrics, II
Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 795-862, January 2024.Abstract We prove that various spaces of constrained positive scalar curvature metrics on compact three‐manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean curvature of the boundary, and our treatment includes both the mean‐convex and the minimal case.
Alessandro Carlotto, Chao Li
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Time‐Dependent Evolving Null Horizons of a Dynamical Spacetime
International Scholarly Research Notices, Volume 2014, Issue 1, 2014., 2014 Totally geodesic null hypersurfaces have been widely used in the study of isolated black holes. In this paper, we introduce a new quasilocal notion of a family of totally umbilical null hypersurfaces called evolving null horizons (ENH) of a dynamical spacetime, satisfied under an appropriate energy condition.
K. L. Duggal +2 more
wiley +1 more source
Totally umbilical hyper-surfaces of the hyperbolic space and the Gauss image(双曲空间中全脐超曲面与高斯映照像)
Zhejiang Daxue xuebao. Lixue ban, 2016 设Mn是单位双曲空间形式Hn+1中定向的紧致无边超曲面.假设存在整数r(1≤r≤n-1）使得高阶平均曲率Hi>0，i=1，2，…，r，且Hr是常数.证明了 ：如果Mn的高斯映照像包含在一个开半球面内，则Mn全脐.
WANGQi(王琪)
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The Morse Index of Sacks–Uhlenbeck α‐Harmonic Maps for Riemannian Manifolds
Journal of Mathematics, Volume 2024, Issue 1, 2024.In this paper, first we prove a nonexistence theorem for α‐harmonic mappings between Riemannian manifolds. Second, the instability of nonconstant α‐harmonic maps is studied with regard to the Ricci curvature criterion of their codomain. Then, we estimate the Morse index for measuring the degree of instability of some particular α‐harmonic maps ...
Amir Shahnavaz +3 more
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New Characterizations of Hyperspheres and Spherical Hypercylinders in Euclidean Space
Journal of Mathematics, Volume 2024, Issue 1, 2024.Let x be an isometric immersion of a Riemannian n‐manifold M into a Euclidean (n + 1)‐space En+1 which does not pass through the origin of En+1. Then, the tangential part of the position vector field x of x is called the canonical vector field, and the normal part gives rise to a scalar function called the support function.
Nasser Bin Turki +3 more
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Totally umbilical CMC hypersurfaces of a conformally recurrent manifold
, 2001 It has been shown that a non-degenerate totally umbilical constant mean curvature hypersurface of a conformally recurrent pseudo Riemannian manifold is conformally ...
Sharma, R., Tarafdar, M.
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Foliations by spacelike hypersurfaces on Lorentz manifolds
, 2023 In this work we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and apply it to investigate conditions for the leaves being totally ...
da Silva, Euripedes Carvalho +1 more
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