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Quasi-Einstein manifolds admitting conformal vector fields

Volume 174 / 2023

Rahul Poddar, S. Balasubramanian, Ramesh Sharma Colloquium Mathematicum 174 (2023), 81-87 MSC: Primary 53C21; Secondary 53C25. DOI: 10.4064/cm8903-6-2023 Published online: 5 October 2023

Abstract

We study an $m$-quasi-Einstein manifold $(M,g,f,\lambda )$ with finite $m$, and a non-homothetic conformal vector field $U$ that leaves the potential vector field and the scalar curvature both invariant, and show that either $M$ is trivial, or $U$ is Killing on the set of regular points of $f$. In the case when $M$ is a gradient Ricci soliton, it is trivial. Finally, for an $m$-quasi-Einstein manifold with finite $m$, and a homothetic vector field $U$ leaving the potential vector field invariant, we show that either (i) $M$ is Ricci-flat and $f$ is constant, or (ii) $U$ is Killing.

Authors

  • Rahul PoddarDepartment of Mathematics and Computer Science
    Sri Sathya Sai Institute of Higher Learning
    Prasanthi Nilayam, 515134, AP, India
    e-mail
  • S. BalasubramanianDepartment of Mathematics and Computer Science
    Sri Sathya Sai Institute of Higher Learning
    Prasanthi Nilayam, 515134, AP, India
    e-mail
  • Ramesh SharmaDepartment of Mathematics
    University of New Haven
    West Haven, CT 06516, USA
    e-mail

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