Results 51 to 60 of about 179 (133)
Real hypersurface of a complex space form [PDF]
, 2016 The purpose of the present paper is to give characterization of real hyper- surface of a complex space form. We find conditions for these hypersurfaces to be phi- symmetric and to have eta- parallel curvature tensor.
SAVITRI SHASHIDAR, ., NAGARAJA, H.G.
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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
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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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Quantitative stability for anisotropic nearly umbilical hypersurfaces
, 2019 We prove qualitative and quantitative stability of the following rigidity theorem: the only anisotropic totally umbilical closed hypersurface is the Wulff shape.
Gioffrè, Stefano, De Rosa, Antonio
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AxiomsWe first study the f-biharmonicity of totally umbilical hypersurfaces in a Riemannian manifold of dimension n≥3 and prove that any totally umbilical proper f-biharmonic hypersurface without boundaries in a nonpositively curved manifold must be noncompact.
Ze-Ping Wang, Li-Hua Qin, Xue-Yi Chen
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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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Killing initial data on totally umbilical & compact hypersurfaces
Journal of Geometry and Physics, 2010 20 pages, submitted january ...
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Characterizations of Euclidean Spheres in Terms of the Tangential Part of the Position Vector Field
International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.In this study, we utilize the support function θ and the tangential component ψT of the position vector field ψ to investigate certain properties of spheres on a compact hypersurface in Euclidean space Rn+1. The first characterization expands upon existing results in the literature by removing constraints on the tangential component ψT and employing ...
Mona Bin-Asfour +3 more
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Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds
, 2017 It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere.
Dimiter Vassilev +2 more
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