Diameter estimation of gradient $\rho$-Einstein solitons

Abstract

Our aim in this article is to give a lower bound of the diameter of a compact gradient $\rho$-Einstein soliton satisfying some given conditions. We have also deduced some conditions of the gradient $\rho$-Einstein soliton with bounded Ricci curvature to become non-shrinking and non-expanding. Further, we have proved that a complete non-compact gradient shrinking or expanding Schouten soliton with non-constant potential and a boundedness condition on scalar curvature must be non-parabolic.

11 pages

References in corpus (3)

• Some characterizations of $\rho$-Einstein solitons
• On complete gradient Schouten solitons
• Isometry theorem of gradient Shrinking Ricci solitons