• Fulltext


        Click here to view fulltext PDF

      Permanent link:

    • Keywords


      Ricci soliton; scalar curvature; Ricci flat; convex function; critical point; Riemannian manifold.

    • Abstract


      In this paper, we consider theRicci curvature of a Ricci soliton. In particular,we have showed that a complete gradient Ricci soliton with non-negative Ricci curvature possessing a non-constant convex potential function having finite weighted Dirichlet integral satisfying an integral condition is Ricci flat and also it isometrically splits a line. We have also proved that a gradient Ricci soliton with non-constant concave potential function and bounded Ricci curvature is non-shrinking and hence the scalar curvaturehas at most one critical point.

    • Author Affiliations



      1. Department of Mathematics, University of Burdwan, Golapbag, Burdwan 713 104, India
    • Dates

  • Proceedings – Mathematical Sciences | News

    • Editorial Note on Continuous Article Publication

      Posted on July 25, 2019

      Click here for Editorial Note on CAP Mode

© 2021-2022 Indian Academy of Sciences, Bengaluru.