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THE k-ALMOST RICCI SOLITONS AND CONTACT GEOMETRY

  • Received : 2017.02.07
  • Accepted : 2017.10.25
  • Published : 2018.01.01

Abstract

The aim of this article is to study the k-almost Ricci soliton and k-almost gradient Ricci soliton on contact metric manifold. First, we prove that if a compact K-contact metric is a k-almost gradient Ricci soliton, then it is isometric to a unit sphere $S^{2n+1}$. Next, we extend this result on a compact k-almost Ricci soliton when the flow vector field X is contact. Finally, we study some special types of k-almost Ricci solitons where the potential vector field X is point wise collinear with the Reeb vector field ${\xi}$ of the contact metric structure.

Keywords

Acknowledgement

Supported by : Council of Scientific and Industrial Research

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