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Monatshefte für Mathematik

, Volume 179, Issue 2, pp 305–320 | Cite as

Quasi-Einstein manifolds endowed with a parallel vector field

  • João F. Silva FilhoEmail author
Article

Abstract

The main of this article is to investigate quasi-Einstein manifolds endowed with a parallel vector field. Here, we obtain some characterizations for this class of manifolds under this condition. Moreover, we prove a rigidity result for quasi-Einstein manifolds endowed with a parallel vector field.

Keywords

Warped products Parallel vector fields Einstein metrics 

Mathematical Subject Classification

Primary 53C25 53C20 53C21 Secondary 53C65 

Notes

Acknowledgments

The author is grateful to E. Ribeiro Jr for many helpful conversations during the elaboration of this paper. Moreover, the author want to thank the referees for their careful reading and helpful suggestions.

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Copyright information

© Springer-Verlag Wien 2015

Authors and Affiliations

  1. 1.UNILAB-Instituto de Ciências exatas e da Natureza, Campus dos PalmaresAcarapeBrazil

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