The k-almost Ricci solitons and contact geometry

TL;DR

This paper investigates the properties of k-almost Ricci solitons on contact metric manifolds, establishing conditions under which such manifolds are isometric to spheres and exploring special cases related to the Reeb vector field.

Contribution

It proves that compact K-contact manifolds as k-almost gradient Ricci solitons are isometric to spheres and extends this to cases where the flow vector field is contact, also analyzing cases with collinearity with the Reeb vector.

Findings

Compact K-contact manifolds as k-almost gradient Ricci solitons are isometric to spheres.

Extension of results to compact k-almost Ricci solitons with contact flow vector fields.

Analysis of k-almost Ricci solitons with potential vector fields collinear with the Reeb vector.

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 S2n+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 soliton where the potential vector field X is point wise collinear with the Reeb vector field {\xi} of the contact metric structure.