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Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 13 (2018), 237 -- 250

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This work is licensed under a Creative Commons Attribution 4.0 International License.

SOME RESULTS OF η-RICCI SOLITONS ON (LCS)n-MANIFOLDS

S. K. Yadav, S. K. Chaubey and D. L. Suthar

Abstract. In this paper, we consider an η -Ricci soliton on the (LCS)n-manifolds (M, φ , ξ , η , g) satisfying certain curvature conditions likes: R(ξ , X) · S= 0 and W 2(ξ, X) · S=0. We show that on the (LCS)n-manifolds (M,φ ,ξ ,η ,g), the existence of η -Ricci soliton implies that (M, g) is a quasi-Einstein. Further, we discuss the existence of Ricci solitons with the potential vector field ξ. In the end, we construct the non-trivial examples of η -Ricci solitons on the (LCS)n-manifolds.

2010 Mathematics Subject Classification: 53C15; 53C21; 53C25.
Keywords: η -Ricci soliton; Quasi-Einstein; (LCS)n-manifold; Ricci tensors; Curvature tensors.

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S. K. Yadav
Department of Mathematics, Poornima College of Engineering, Jaipur, 302022, Rajasthan, India.
e-mail: prof_sky16@yahoo.com

S. K. Chaubey
Section of Mathematics, Department of Information Technology, Shinas College of Technology, Oman.
e-mail: sk22_math@yahoo.co.in

D. L. Suthar
Department of Mathematics, Wollo University, P. O. Box: 1145, Dessie, South Wollo, Ethopia.
e-mail: dlsuthar@gmail.com


http://www.utgjiu.ro/math/sma