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Quasi-Einstein structures and almost cosymplectic manifolds

  • Xiaomin ChenEmail author
Original Paper
  • 11 Downloads

Abstract

In this article, we study almost cosymplectic manifolds admitting quasi-Einstein structures \((g, V, m, \lambda )\). First we prove that an almost cosymplectic \((\kappa ,\mu )\)-manifold is locally isomorphic to a Lie group if \((g, V, m, \lambda )\) is closed and on a compact almost \((\kappa ,\mu )\)-cosymplectic manifold there do not exist quasi-Einstein structures \((g, V, m, \lambda )\), in which the potential vector field V is collinear with the Reeb vector field \(\xi \). Next we consider an almost \(\alpha \)-cosymplectic manifold admitting a quasi-Einstein structure and obtain some results. Finally, for a K-cosymplectic manifold with a closed, non-steady quasi-Einstein structure, we prove that it is \(\eta \)-Einstein. If \((g, V, m, \lambda )\) is non-steady and V is a conformal vector field, we obtain the same conclusion.

Keywords

Quasi-Einstein structures Almost cosymplectic \((\kappa {, } \mu )\)-manifolds Almost \(\alpha \)-cosymplectic manifolds Cosymplectic manifolds Einstein manifolds 

Mathematics Subject Classification

53C25 53D15 

Notes

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Copyright information

© The Royal Academy of Sciences, Madrid 2020

Authors and Affiliations

  1. 1.College of ScienceChina University of Petroleum (Beijing)BeijingChina

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