Existence of Finite Global Norm of Potential Vector Field in a Ricci Soliton

Abstract

In this paper, we present global norm of potential vector field in Ricci soliton. In particular, we deduce certain conditions so that the potential vector field has finite global norm in expanding Ricci soliton. In addition, we show that if the potential vector field has finite global norm in complete non-compact Ricci soliton having finite volume, then the scalar curvature becomes constant.