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On the Rigidity of Generalized Quasi-Einstein Manifolds

  • M. Ahmad Mirshafeazadeh
  • B. BidabadEmail author
Article

Abstract

Here, it is shown a compact generalized quasi-Einstein or briefly a GQE manifold has the finite fundamental group. Next, under certain assumptions, a rigidity result shows that a compact GQE manifold is diffeomorphic to the standard n-sphere. As a corollary, if the scalar curvature is constant, then it is isometric to the standard n-sphere. Meanwhile, a trivialization criterion and existence of harmonic vector fields on a GQE are studied.

Keywords

Einstein Generalized quasi-Einstein manifold Ricci soliton Fundamental group Harmonic 

AMS Subject Classification 2010

53C21 53C25 

Notes

Acknowledgements

The first author would like to thank the Institut de Mathématiques de Toulouse (ITM) where this work is partially carried out.

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Computer SciencesAmirkabir University of Technology (Tehran Polytechnic)TehranIran
  2. 2.Institut de Mathématique de ToulouseUniversité Paul SabatierToulouseFrance
  3. 3.Department of MathematicsPayame Noor UniversityTehranIran

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