Ricci Solitons on α-para Kenmotsu Manifolds with Semi Symmetric Metric Connection

Abstract

In this paper we introduce notion of Ricci solitons in α-para Kenmotsu manifold with semi -symmetric metric connection. We have found the relations between curvature tensor, Ricci tensors and scalar curvature of α-para Kenmotsu manifold with semi-symmetic metric connection.We have proved that 3-dimensional α-para Kenmotsu manifold with semi -symmetric metric connection is an η-Einstein manifold and the Ricci soliton defined on
this manifold is named expanding and steady with respect to the value of λ constant.It is proved that Conharmonically flat α-para Kenmotsu manifold
with semi-symmetric metric connection is η-Einstein manifold.

Mathematics Subject Classification: 53C15,53C25,53C40,53C50