Illinois Journal of Mathematics

Some results on compact almost Ricci solitons with null Cotton tensor

A. Barros and I. Evangelista

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Abstract

The aim of this paper is to prove that a compact almost Ricci soliton with null Cotton tensor is isometric to a standard sphere provided one of the following conditions associated to the Schouten tensor holds: the second symmetric function is constant and positive; two consecutive symmetric functions are non null multiple or some symmetric function is constant and the quoted tensor is positive.

Article information

Source
Illinois J. Math., Volume 60, Number 2 (2016), 529-540.

Dates
Received: 16 April 2016
Revised: 29 December 2016
First available in Project Euclid: 11 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1499760020

Digital Object Identifier
doi:10.1215/ijm/1499760020

Mathematical Reviews number (MathSciNet)
MR3680546

Zentralblatt MATH identifier
1368.53036

Subjects
Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20] 53C21: Methods of Riemannian geometry, including PDE methods; curvature restrictions [See also 58J60]
Secondary: 53C24: Rigidity results

Citation

Barros, A.; Evangelista, I. Some results on compact almost Ricci solitons with null Cotton tensor. Illinois J. Math. 60 (2016), no. 2, 529--540. doi:10.1215/ijm/1499760020. https://projecteuclid.org/euclid.ijm/1499760020


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