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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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Some Results on Almost Ricci Solitons and Geodesic Vector Fields.
TL;DR: In this paper, it was shown that a Ricci soliton whose soliton vector field is divergence-free and its soliton soliton is Killing can be reduced to Ricci Soliton if and only if the associated vector field has geodesic this paper.
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Gaussian mean curvature flow
A. A. Borisenko,Vicente Miquel +1 more
TL;DR: In this article, the authors consider the flow of a hypersurface driven by its mean curvature associated to a Gaussian density and give a detailed account of the evolution of convex hypersurfaces under this flow.
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On weakly conformally symmetric manifolds
TL;DR: In this article, it was shown that an Einstein weakly conformally symmetric manifold reduces to a weakly symmetric one, and several examples of non-vanishing scalar curvatures have been obtained.
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Vanishing theorems for the cohomology groups of free boundary submanifolds
TL;DR: In this paper, it was shown that there exists a universal constant C, depending only on positive integers, for compact free boundary submanifolds of dimension n immersed in the Euclidean unit ball whose size of the traceless second fundamental form is less than C.
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Almost $$*$$∗ -Ricci soliton on paraKenmotsu manifolds
TL;DR: In this article, the authors considered the problem of paracontact geometry on a para-Kenmotsu manifold and showed that if the metric g of g of G of σ, σ is a Gaussian, then G is either the potential vector field collinear with Reeb vector field or Ricci soliton.