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On generalized quasi-Einstein manifolds

  • Mir Ahmad Mirshafeazadeh and Behroz Bidabad ORCID logo EMAIL logo
Published/Copyright: March 27, 2018

Abstract

We study generalized quasi-Einstein manifolds, or briefly, GQE manifolds. Here, we present relations between the Bach, Cotton and D tensors on GQE manifolds. Next, a 3-tensor E which measures the deviation of m-quasi-Einstein manifolds from GQE manifolds is introduced. Among others in dimension 3, it is shown that Bach-flatness implies locally conformally flatness. Furthermore, it is proved that, around a regular point of the fourth-order divergence free Weyl tensor, a GQE manifold is a locally warped product manifold with (n-1)-dimensional Einstein fibers in suitable cases.

MSC 2010: 53C21; 53C25

References

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Received: 2017-10-13
Revised: 2018-02-12
Accepted: 2018-03-07
Published Online: 2018-03-27
Published in Print: 2019-07-01

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