## Diameter estimation of gradient $ρ$-Einstein solitons

10 Mar 2021  ·  Absos Ali Shaikh, Prosenjit Mandal, Chandan Kumar Mondal ·

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. read more

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Differential Geometry 53C20, 53C21, 53C25