Articles written in Proceedings – Mathematical Sciences

    • On Ricci solitons whose potential is convex


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      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.

    • Characterization of the potential function of a Ricci soliton


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      In this article, we have studied the behavior of the potential function along some geodesic in a Ricci soliton under some curvature restriction. In particular, we haveshowed that under some curvature restriction, the potential function is reduced to a parabola along some geodesic. Furthermore, we have investigated the change of intersecting angles between the potential vector field and a geodesic in a Ricci soliton. Further, we have deduced the condition when the potential function becomes convex in a shrinking Ricci soliton. Finally, we have concluded the paper by showing the non-existence of convex potential in an expanding Ricci soliton having non-negative Ricci curvature.

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