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http://dx.doi.org/10.4134/JKMS.j170103

THE k-ALMOST RICCI SOLITONS AND CONTACT GEOMETRY  

Ghosh, Amalendu (Department of Mathematics Chandernagore College)
Patra, Dhriti Sundar (Department of Mathematics Jadavpur University)
Publication Information
Journal of the Korean Mathematical Society / v.55, no.1, 2018 , pp. 161-174 More about this Journal
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
contact metric manifold; k-almost Ricci soliton; k-almost gradient Ricci soliton; K-contact manifold; Sasakian manifold; Einstein manifold;
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