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Geometriae Dedicata

, Volume 169, Issue 1, pp 225–237 | Cite as

Some triviality results for quasi-Einstein manifolds and Einstein warped products

Original Paper

Abstract

In this paper we prove a number of triviality results for Einstein warped products and quasi-Einstein manifolds using different techniques and under assumptions of various nature. In particular we obtain and exploit gradient estimates for solutions of weighted Poisson-type equations and adaptations to the weighted setting of some Liouville-type theorems.

Keywords

Einstein warped products Quasi-Einstein manifolds  Triviality  Gradient estimates 

Mathematics Subject Classification (2000)

53C21 

Notes

Acknowledgments

We wish to thank Stefano Pigola and Jeffrey Case for valuable suggestions and useful comments on earlier versions of the paper. We thank the anonymous referee for useful suggestions that helped to improve the exposition. The first author would also like to thank Francesca Savini for some useful remarks.

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanItaly
  2. 2.Dipartimento di Scienza e Alta TecnologiaUniversità degli Studi dell’InsubriaComoItaly

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