Communications in Analysis and Geometry

Volume 28 (2020)

Number 3

Remarks on complete noncompact Einstein warped products

Pages: 547 – 563

DOI: https://dx.doi.org/10.4310/CAG.2020.v28.n3.a3

Authors

R. Batista (Departamento de Matemática, Universidade Federal do Piauí – UFPI, Teresina, PI, Brazil)

M. Ranieri (Instituto de Matemática, Universidade Federal de Alagoas – UFAL, Maceió, AL, Brazil)

E. Ribeiro, Jr. (Departamento de Matemática,Universidade Federal do Ceará – UFC, Fortaleza, CE, Brazil)

Abstract

The purpose of this article is to investigate the structure of complete non-compact quasi-Einstein manifolds. We show that complete noncompact quasi-Einstein manifolds with $\lambda = 0$ are connected at infinity. In addition, we provide some conditions under which quasi-Einstein manifolds with $\lambda \lt 0$ are $f$-non-parabolic. In particular, we obtain estimates on volume growth of geodesic balls for such manifolds.

Full Text (PDF format)

R. Batista was partially supported by CNPq/Brazil, Grant: 310881/2017-0.

M. Ranieri was partially supported by CAPES/Brazil.

E. Ribeiro Jr. was partially supported by CNPq/Brazil, Grant: 303091/2015-0.

Received 27 August 2015

Accepted 4 December 2018

Published 6 July 2020