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Communications in Analysis and Geometry
Volume 28 (2020)
Remarks on complete noncompact Einstein warped products
Pages: 547 – 563
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.
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