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 paper, an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient were obtained for the Kaehler manifold.
Abstract: We obtain an intrinsic formula of a Ricci soliton vector field and a differential condition for the non-steady case to be gradient. Next we provide a condition for a Ricci soliton on a Kaehler manifold to be a Kaehler–Ricci soliton. Finally we give an example supporting the first result.
4 citations
4 citations
01 Jan 2021
TL;DR: In this article, the authors obtained some results on almost Einstein solitons with unit geodesic potential vector field and provided necessary and sufficient conditions for the soliton to be trivial.
Abstract: We obtain some results on almost Einstein solitons with unit geodesic potential vector field and provide necessary and sufficient conditions for the soliton to be trivial.
4 citations
TL;DR: In this article, an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CRdimension immersed in a unit (2m+1)-sphere was derived.
Abstract: In this paper we derive an integral formula on an (n + 1)-dimensional, compact, minimal contact CR-submanifold M of (n - 1) contact CR-dimension immersed in a unit (2m+1)-sphere . Using this integral formula, we give a sufficient condition concerning with the scalar curvature of M in order that such a submanifold M is to be a generalized Clifford torus.
4 citations