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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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Submanifolds of a Riemannian manifold with semisymmetric metric connections
TL;DR: In this article, the authors derived the Gauss curvature equation and the CodazziMainardi equation with respect to a semisymmetric metric connection on a Riemannian manifold and the induced one on a submanifold.
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A new connection in a Riemannian manifold
TL;DR: In this article, the existence of a new connection in a Riemannian manifold is proved and the curvature tensor of the new connection is also found, where the connection reduces to several symmetric, semi-symmetric and quarter symmetric connections; even some of them are not introduced so far.
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Contact metric manifolds with η-parallel torsion tensor
TL;DR: In this article, it was shown that a non-Sasakian contact metric manifold with η-parallel torsion tensor and sectional curvatures of plane sections containing the Reeb vector field different from 1 at some point, is a (k, μ)-contact manifold.
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Hypersurfaces of a Riemannian manifold with semiSlmmetric non-metric connection
Uday Chand De,D. Kamilya +1 more
TL;DR: In this paper, the properties of hypersurfaces of a Riemannian manifold with a semi-symmetric non-metric connection were studied and the authors extended the work of Agashe and Chafle.
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Exact Einstein scalar field solutions for formation of black holes in a cosmological setting
TL;DR: In this paper, two classes of exact solutions to Einstein's equations are obtained: the first class corresponds to the minimal coupling, the second one to the conformal coupling, and it is shown that there is a critical value for a parameter on which the solution depends.