• Fulltext

       

        Click here to view fulltext PDF


      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/130/0055

    • 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

       

      CHANDAN KUMAR MONDAL1 ABSOS ALI SHAIKH1

      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.