• ABSOS ALI SHAIKH

      Articles written in Proceedings – Mathematical Sciences

    • On Ricci solitons whose potential is convex

      CHANDAN KUMAR MONDAL ABSOS ALI SHAIKH

      More Details Abstract Fulltext PDF

      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.

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