• Characterization of the potential function of a Ricci soliton

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    • Keywords


      Ricci soliton; Busemann function; Riemannian manifold.

    • Abstract


      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.

    • Author Affiliations



      1. Department of Mathematics, School of Sciences, Netaji Subhas Open University, Durgapur Regional Center, Durgapur 713 214, India
    • Dates

  • Proceedings – Mathematical Sciences | News

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      Posted on July 25, 2019

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