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��-RICCI SOLITONS ON �� - LP-SASAKIAN MANIFOLDS WITH A QUARTER-SYMMETRIC METRIC CONNECTION

  • Haseeb, Abdul (Department of Mathematics, Faculty of Science, Jazan University) ;
  • Prasad, Rajendra (Department of Mathematics and Astronomy, University of Lucknow)
  • Received : 2018.12.05
  • Accepted : 2019.02.23
  • Published : 2019.09.25

Abstract

In this paper, we study ${\eta}$-Ricci solitons on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions. In particular, we have discussed that the Ricci soliton on ${\epsilon}$-LP-Sasakian manifolds with a quarter-symmetric metric connection satisfying certain curvature conditions is expanding or steady according to the vector field ${\xi}$ being timelike or spacelike. Moreover, we construct 3-dimensional examples of an ${\epsilon}$-LP-Sasakian manifold with a quarter-symmetric metric connection to verify some results of the paper.

Keywords

${\eta}$-Ricci solitons;${\epsilon}$-LP-Sasakian;quarter-symmetric metric connection

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