Rigidity of (m,ρ)-quasi Einstein manifolds

Sezgin Altay Demirbağ, Sinem Güler*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This paper deals with the study on (m,ρ)-quasi Einstein manifolds. First, we give some characterizations of an (m,ρ)-quasi Einstein manifold admitting closed conformal or parallel vector field. Then, we obtain some rigidity conditions for this class of manifolds. We prove that an (m,ρ)-quasi Einstein manifold with a closed conformal vector field has a warped product structure of the form (Formula presented.), where I is a real interval, (M*,g*) is an (n-1) -dimensional Riemannian manifold and q is a smooth function on I. Finally, a non-trivial example of an (m,ρ) -quasi Einstein manifold verifying our results in terms of the potential function is presented.

Original languageEnglish
Pages (from-to)2100-2110
Number of pages11
JournalMathematische Nachrichten
Volume290
Issue number14-15
DOIs
Publication statusPublished - Oct 2017

Bibliographical note

Publisher Copyright:
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Keywords

  • (m,ρ)-quasi Einstein manifold
  • 53B15
  • 53B20
  • 53C21
  • 53C25
  • closed conformal vector field
  • conformal mapping
  • warped product

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