A Study on Ricci Solitons in Generalized Complex Space Form

Abstract

In this paper we obtain the condition for the existence of Ricci solitons in non-flat generalized complex space form by using Eisenhart problem. Also it is proved that if (g, V, λ) is Ricci soliton then V is solenoidal if and only if it is shrinking or steady or expanding depending upon the sign of scalar curvature.

Keywords

• Kähler manifolds
• generalized complex space form
• parallel second order covariant tensor field
• Einstein space
• Ricci soliton