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The present paper deals with a study of infinitesimal $CL$-transformations on Kenmotsu manifolds, whose metric is Yamabe soliton and obtained sufficient conditions for such solitons to be expanding, steady and shrinking. Among others, we find a necessary and sufficient condition of a Yamabe soliton on Kenmotsu manifold with respect to $CL$-connection to be Yamabe soliton on Kenmotsu manifold with respect to Levi-Civita connection. We found the necessary and sufficient condition for the Yamabe soliton structure to be invariant under Schouten-Van Kampen connection. Finally, we constructed an example of steady Yamabe soliton on $3$-dimensional Kenmotsu manifolds with respect to Schouten-Van Kampen connection.
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참고문헌 (20)
참고문헌 신청
E. Barbosa / 2013 / On conformal solutions of the Yamabe flow / Arch. Math. (Basel) 101(1):79~89
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry / Springer-Verlag
D. Chakraborty / 2018 / Ricci solitons on three dimensional β-Kenmotsu manifolds with respect to Schouten-Van Kampen connection / J. Ultra Scientist of Physical Sciences 30(1):86~91
S. Debnath / 2012 / Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton / Lobachevskii J. Math 33(4):312~316
K. Erken / 2017 / Yamabe solitons on three-dimensional normal almost para-contact metric manifolds / arXiv: 1708. 04882v2. [math. DG]
D. E. Blair / 1976 / Contact Manifolds in Riemannian Geometry / Springer-Verlag
D. Chakraborty / 2018 / Ricci solitons on three dimensional β-Kenmotsu manifolds with respect to Schouten-Van Kampen connection / J. Ultra Scientist of Physical Sciences 30(1):86~91
S. Debnath / 2012 / Second order parallel tensor in trans-Sasakian manifolds and connection with Ricci soliton / Lobachevskii J. Math 33(4):312~316
K. Erken / 2017 / Yamabe solitons on three-dimensional normal almost para-contact metric manifolds / arXiv: 1708. 04882v2. [math. DG]
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