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
TL;DR: In this paper, the authors introduced the concept of h-almost Ricci soliton, which extends naturally the almost Ricci solution by Pigola-Rigoli-Rimoldi-Setti.
29 citations
TL;DR: In this article, the authors constructed a strong Laplacian by using the third operator in the basis of natural first-order operators acting on the differential forms of a Riemannian manifold.
Abstract: We construct a strong Laplacian D
*
D by using the third operator in the basis {d,d
*,D} of the space of natural first-order operators acting on the differential forms of a Riemannian manifold (M,g). We study the properties of the Laplacian D
*
D and obtain Weitzenbock's formula relating the three strong Laplacians dd
*, d
*
d, and D
*
D to the curvature of the manifold (M,g).
27 citations
TL;DR: In this paper, it was shown that a compact locally conformally flat almost Ricci soliton is isometric to Euclidean space and a standard sphere, provided an integral condition holds.
Abstract: In this paper, we show that either, a Euclidean space $\mathbb{R}^{n}$, or a standard sphere $\mathbb{S}^{n}$, is the unique manifold with nonnegative scalar curvature which carries a structure of a gradient almost Ricci soliton, provided this gradient is a non trivial conformal vector field. Moreover, in the spherical case the field is given by the first eigenfunction of the Laplacian. Finally, we shall show that a compact locally conformally flat almost Ricci soliton is isometric to Euclidean sphere $\mathbb{S}^{n}$ provided an integral condition holds.
27 citations
TL;DR: The work in this paper was supported by the Fundacao para a Ciencia e Tecnologia (Portugal), throught the grant SFRH/BD/22211/2005, and, in its final stages, by the Cambridge Philosophical Society.
Abstract: This work was supported by the Fundacao para a Ciencia e Tecnologia (Portugal), throught the grant SFRH/BD/22211/2005, and, in its final stages, by the Cambridge Philosophical Society.
26 citations
TL;DR: In this article, a generalized Sasakian space form admits conformal Ricci soliton and quasi-Yamabe soliton, and it is shown that the potential function of a conformal gradient Ricci s soliton is constant.
25 citations