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Integral formulas in riemannian geometry
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This article is published in Bulletin of The London Mathematical Society.The article was published on 1973-03-01. It has received 331 citations till now. The article focuses on the topics: Riemannian geometry & Fundamental theorem of Riemannian geometry.read more
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Kinematics of Hypersurfaces in Riemannian Manifolds
N. Kadianakis,F. Travlopanos +1 more
TL;DR: In this paper, the kinematics of an m-dimensional continuum moving in an (m+1)-dimensional ambient space, modelled by the motion of a hypersurface M in a Riemannian manifold N, are studied.
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Integral inequalities in Kählerian manifolds and their applications
TL;DR: A vector field v h is called a holomorphically projective (or H-projective, for brevity) vector field if it satisfies the following properties: 1) The Ricci tensor and the scalar curvature of V h.
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Almost Hermitian manifolds admitting holomorphically planar conformal vector fields
Amalendu Ghosh,Ramesh Sharma +1 more
TL;DR: In this paper, an almost Hermitian manifold M admits a holomorphically planar conformal vector (HPCV) field (a generalization of a closed conformal field) V.
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Implications of energy conditions on standard static space–times
Fernando Dobarro,Bülent Ünal +1 more
TL;DR: In this article, a family of sufficient or necessary conditions for a set of physically reasonable energy and convergence conditions in relativity and related theories is given. But the authors focus on questions about the subharmonicity of the warping function, the scalar curvature map, conformal hyperbolicity, conjugate points and the time-like diameter of this class of space-times.
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Stability of area-preserving variations in space forms
Yijun He,Yijun He,Haizhong Li +2 more
TL;DR: In this article, the area-preserving variational problem for compact hypersurfaces without boundary immersed in space forms was studied and it was shown that they are r-stable if and only if they are totally umbilical hypersurface.