Integral formulas in riemannian geometry
01 Mar 1973-Bulletin of The London Mathematical Society (Oxford University Press (OUP))-Vol. 5, Iss: 1, pp 124-125
About: 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.
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01 Jan 2013
TL;DR: In this article, a Sasakian manifold with quasi-conformal curvature tensors was studied and the object of the paper was to study the curvatures of the manifold.
Abstract: The object of the paper is to study a Sasakian manifold with quasi-conformal curvature tensor.
16 citations
TL;DR: In this article, the authors obtained sufficient conditions for a 3D compact trans-Sasakian manifold of type α, β to be homothetic to a cosymplectic manifold.
Abstract: In this paper, we obtain some sufficient conditions for a 3-dimensional compact trans-Sasakian manifold of type (α, β) to be homothetic to a Sasakian manifold. A characterization of a 3-dimensional cosymplectic manifold is also obtained.
16 citations
TL;DR: In this article, the curvature inheritance symmetry (CI) for string cloud and string fluid in the context of general relativity was studied, and it was shown that a proper CI (i.e., α ≠ 0) is also a conformal Killing vector.
Abstract: We study, in this paper, curvature inheritance symmetry (CI), , where α is a scalar function, for string cloud and string fluid in the context of general relativity. Also, we have obtained some result when a proper CI (i.e., α ≠ 0) is also a conformal Killing vector.
16 citations
TL;DR: In this paper, the authors provide a global characterization of the Killing vector fields of a standard static space-time by a system of partial differential equations, where the Riemannian part is compact.
16 citations
01 Jan 2005
TL;DR: In this paper, the authors studied the properties of weakly Ricci symmetric manifold (W RS)n and proved that W RSn is isometric to a sphere in En+1.
Abstract: The object of the present paper is to study some global properties of a weakly Ricci symmetric manifold (W RS)n. Among others, it is proved that if a compact, orientable (W RS)n of constant scalar curvature without boundary admits a nonisometric conformal transformation, then the (W RS)n is isometric to a sphere. Also we obtain a sucien t condition for a compact, orientable (W RS)n without boundary to be conformal to a sphere in En+1. It is also proved that in a compact, orientable conformally at (W RS)n(n > 3) certain p-th Betti number vanish.
16 citations