V. Venkatesha ; H. Aruna Kumara - Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

cm:9695 - Communications in Mathematics, September 19, 2022, Volume 30 (2022), Issue 1 - https://doi.org/10.46298/cm.9695
Quasi Yamabe Solitons on 3-Dimensional Contact Metric Manifolds with Q\varphi=\varphi Q

Authors: V. Venkatesha ; H. Aruna Kumara

In this paper we initiate the study of quasi Yamabe soliton on 3-dimensional contact metric manifold with Q\varphi=\varphi Q and prove that if a 3-dimensional contact metric manifold M such that Q\varphi=\varphi Q admits a quasi Yamabe soliton with non-zero soliton vector field V being point-wise collinear with the Reeb vector field {\xi}, then V is a constant multiple of {\xi}, the scalar curvature is constant and the manifold is Sasakian. Moreover, V is Killing. Finally, we prove that if M is a 3-dimensional compact contact metric manifold such that Q\varphi=\varphi Q endowed with a quasi Yamabe soliton, then either M is flat or soliton is trivial.


Volume: Volume 30 (2022), Issue 1
Published on: September 19, 2022
Accepted on: July 3, 2020
Submitted on: June 24, 2019
Keywords: Mathematics - Differential Geometry


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