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Triviality of Compact m-Quasi-Einstein Manifolds

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Abstract

The goal of this note is to show that a compact m-quasi-Einstein manifold \({(M^{n}, g, X, \lambda)}\) has the vector field X identically zero provided that \({(M^{n}, g)}\) is an Einstein manifold.

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References

  1. Barros A., Gomes J.N.: A compact gradient generalized quasi-Einstein metric with constant scalar curvature. J. Math. Anal. Appl. (Print) 401, 702–705 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  2. Barros A., Gomes J.N., Ribeiro E.: A note on rigidity of the almost Ricci soliton. Arch. Math. 100, 481–490 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barros A., Ribeiro E. Jr: Some characterizations for compact almost Ricci solitons. Proc. Am. Math. Soc. 140, 1033–1040 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Barros A., Ribeiro E. Jr: Characterizations and integral formulae for generalized quasi-Einstein metrics. Bull. Braz. Math. Soc. 45, 325–341 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  5. Barros A., Ribeiro E. Jr, Silva J.F.: Uniqueness of quasi-Einstein metrics on 3-dimensional homogeneous Riemannian manifolds. Differ. Geom. Appl. 35, 60–73 (2014)

    Article  MATH  Google Scholar 

  6. Besse A.: Einstein Manifolds. Springer, Berlin (1987)

    Book  MATH  Google Scholar 

  7. Case J., Shu Y., Wei G.: Rigidity of quasi-Einstein metrics. Differ. Geom. Appl. 29, 93–100 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Hamilton, R.: The Ricci Flow on Surfaces. Contemporary Mathematics, vol. 71, pp. 237–262. AMS, Providence (1988)

  9. Kazdan J., Warner F.: Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvature. Ann. Math. 101, 317–331 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  10. Pigola, S., Rigoli, M., Rimoldi, M., Setti, A.: Ricci Almost Solitons. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) X, 757–799 (2011)

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Authors and Affiliations

  1. Departamento de Matemática, UFC, 60455-760, Fortaleza, CE, Brazil

    Abdênago A. Barros

  2. Departamento de Matemática, UFAM, 69077-000, Manaus, AM, Brazil

    José N. V. Gomes

Authors
  1. Abdênago A. Barros
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  2. José N. V. Gomes
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Corresponding author

Correspondence to José N. V. Gomes.

Additional information

A. A. Barros and J. N. V. Gomes are partially supported by CNPq-BR.

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Barros, A.A., Gomes, J.N.V. Triviality of Compact m-Quasi-Einstein Manifolds. Results Math 71, 241–250 (2017). https://doi.org/10.1007/s00025-016-0556-5

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  • DOI: https://doi.org/10.1007/s00025-016-0556-5

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