Some characterizations for compact almost Ricci solitons

Barros, A.; Jr., E. Ribeiro

doi:10.1090/S0002-9939-2011-11029-3

Some characterizations for compact almost Ricci solitons
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by A. Barros and E. Ribeiro Jr. PDF

Proc. Amer. Math. Soc. 140 (2012), 1033-1040 Request permission

Abstract:

The aim of this paper is to find some equations of structure for almost Ricci solitons which generalize the equivalent for Ricci solitons. As a consequence of these equations we derive an integral formula for the compact case which enables us to show that a compact nontrivial almost Ricci soliton is isometric to a sphere provided either it has constant scalar curvature or its associated vector field is conformal. Moreover, we also use the Hodge-de Rham decomposition theorem to make a link with the associated vector field of an almost Ricci soliton.

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