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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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Curvature Inheritance Symmetry In Riemannian Spaces with Applications to String Cloud and String Fluids
TL;DR: In this paper, the curvature inheritance symmetry (CI) was studied for string clouds and string fluid in the context of general relativity, and the authors obtained some results when a proper CI (i.e., $\alpha
eq 0$) is also a conformal Killing vector.
Journal ArticleDOI
m-quasi-Einstein metric and contact geometry
TL;DR: In this paper, the existence of a closed m-quasi-Einstein metric on a complete K-contact manifold was shown to be Sasakian and Einstein provided a constant multiple of the Reeb vector field.
Journal ArticleDOI
A sub-elliptic estimate for a class of invariantly defined elliptic systems
Lesley Sibner,Robert Sibner +1 more
TL;DR: In this paper, the authors consider a nonlinear system of partial differential equations on a Riemannian manifold and obtain a sub-elliptic estimate for the speed of the flow in terms of the curvature of the manifold.
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Stability of hypersurfaces with constant $r$-th anisotropic mean curvature
Yijun He,Haizhong Li +1 more
TL;DR: In this paper, the authors define the $r$-th anisotropic mean curvature function (H^F_r$ ) for hypersurfaces in a closed hypersurface with a positive function on a convexity condition, and show that the Wulff shape of the positive function is stable if and only if
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On almost pseudo-conformally symmetric Ricci-recurrent manifolds with applications to relativity
Uday Chand De,Avik De +1 more
TL;DR: In this article, the existence of almost pseudo-conformally symmetric Ricci-recurrent manifold has been proved by an explicit example and some geometric properties have been studied.