scispace - formally typeset
Search or ask a question
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.
Citations
More filters
Journal ArticleDOI
TL;DR: In this paper, the principal curvatures of a hypersurface M are defined as isoparametric functions and the set (ρ 1,...,ρ n ) defines an isoparomorphic system.
Abstract: Let x:M→\(\) be an isometric immersion of a hypersurface M into an (n+1)-dimensional Riemannian manifold \(\) and let ρ i (i∈{1,...,n}) be the principal curvatures of M. We denote by E and P the distinguished vector field and the curvature vector field of M, respectively, in the sense of [8].¶If M is structured by a P-parallel connection [7], then it is Einsteinian. In this case, all the curvature 2-forms are exact and other properties induced by E and P are stated.¶The principal curvatures ρ i are isoparametric functions and the set (ρ1,...,ρ n ) defines an isoparametric system [10].¶In the last section, we assume that, in addition, M is endowed with an almost symplectic structure. Then, the dual 1-form π=P♭ of P is symplectic harmonic. If M is compact, then its 2nd Betti number b2≥1.

1 citations

Journal ArticleDOI
13 Feb 2021
TL;DR: In this paper, Bach almost soliton on Riemannian manifold satisfying certain conditions on the potential vector field was studied and the Bach almost-soliton was introduced and studied.
Abstract: We introduced and studied Bach almost soliton on Riemannian manifold satisfying certain conditions on the potential vector field.

1 citations

01 Jan 2014
TL;DR: In this article, the authors study Sasakian manifold whose metric is as Yamabe soliton and obtain some properties of this manifold, which is known as the Yamabe manifold.
Abstract: In this paper we study Sasakian manifold whose metric is as Yamabe soliton and obtain some

1 citations