Ricci solitons on ε-Sasakian manifold under Da-homothetic deformation

Abstract

The objective of the present paper is to study Da-homothetic deformation of ε-sasakian manifold. We have analyzed ε-sasakian metric as Ricci soliton based on the associated vector field, by taking the vector field as orthogonal to Reeb vector field which results in constant scalar curvature. We have also shown that the vector field V transforms (1,1) tensor field φ, 1-form η and Reeb vector field ξ. Further we have shown that η-Einstein Ricci soliton and η-Einstein ρ Ricci soliton remains η-Einstein Ricci soliton with constant scalar curvature.