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Journal ArticleDOI

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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TL;DR: In this article, the authors studied some properties of a quasi-Einstein manifold, and a non-trivial concrete example of such a manifold is also given, where the properties of the manifold are investigated.
Abstract: The object of the present paper is to study some properties of a quasi Einstein manifold. A non-trivial concrete example of a quasi Einstein manifold is also given.

36 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if a compact K-contact metric is a gradient Ricci almost soliton, then it is isometric to a unit sphere S 2n+1.
Abstract: We show that if a compact K-contact metric is a gradient Ricci almost soliton, then it is isometric to a unit sphere S 2n+1. Next, we prove that if the metric of a non-Sasakian (κ, μ)-contact metric is a gradient Ricci almost soliton, then in dimension 3 it is flat and in higher dimensions it is locally isometric to E n+1 × S n (4). Finally, a couple of results on contact metric manifolds whose metric is a Ricci almost soliton and the potential vector field is point wise collinear with the Reeb vector field of the contact metric structure were obtained.

36 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the Sasakian metric on the Heisenberg group H 2 n + 1 is a non-trivial Ricci soliton of such type, and that if an η -Einstein contact metric manifold has a vector field V leaving the structure tensor and the scalar curvature invariant, then either V is an infinitesimal automorphism, or M is D -homothetically fixed K -contact.

35 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.
Abstract: Abstract In this paper, we prove that if a 3-dimensional cosymplectic manifold M3 admits a Ricci soliton, then either M3 is locally flat or the potential vector field is an infinitesimal contact transformation.

34 citations