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Bounds on volume growth of geodesic balls for Einstein warped products


Authors: A. Barros, R. Batista and E. Ribeiro Jr.
Journal: Proc. Amer. Math. Soc. 143 (2015), 4415-4422
MSC (2010): Primary 53C25, 53C20, 53C21; Secondary 53C65
DOI: https://doi.org/10.1090/S0002-9939-2015-12606-8
Published electronically: April 1, 2015
MathSciNet review: 3373940
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Abstract: The purpose of this note is to provide some volume estimates for Einstein warped products similar to a classical result due to Calabi and Yau for complete Riemannian manifolds with nonnegative Ricci curvature. To do so, we make use of the approach of quasi-Einstein manifolds which is directly related to Einstein warped products. In particular, we present an obstruction for the existence of such a class of manifolds.


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Additional Information

A. Barros
Affiliation: Universidade Federal do Ceará - UFC, Departamento de Matemática, Campus do Pici, Av. Humberto Monte, Bloco 914, 60455-760-Fortaleza/CE, Brazil
Email: abbarros@mat.ufc.br

R. Batista
Affiliation: Universidade Federal do Piauí - UFPI, Departamento de Matemática, Campus Petrônio Portella, 64049-550-Teresina /PI, Brazil
Email: rmarcolino@ufpi.edu.br

E. Ribeiro Jr.
Affiliation: Universidade Federal do Ceará - UFC, Departamento de Matemática, Campus do Pici, Av. Humberto Monte, Bloco 914, 60455-760-Fortaleza/CE, Brazil
Address at time of publication: Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Email: ernani@mat.ufc.br

DOI: https://doi.org/10.1090/S0002-9939-2015-12606-8
Keywords: Quasi-Einstein manifolds, warped product, Einstein metrics, volume estimates
Received by editor(s): May 2, 2014
Received by editor(s) in revised form: May 3, 2014, and July 4, 2014
Published electronically: April 1, 2015
Additional Notes: The first and second authors were partially supported by grants from CNPq/Brazil
The third author was partially supported by grants from PJP-FUNCAP/Brazil and CNPq/Brazil
Communicated by: Lei Ni
Article copyright: © Copyright 2015 American Mathematical Society