Geometric properties of second Ricci solitons

TL;DR

This paper introduces the concept of second Ricci solitons, explores their geometric properties on various manifolds, and investigates their behavior in immersed submanifolds and warped products.

Contribution

It is the first to define and analyze second Ricci solitons, expanding the understanding of Ricci soliton structures in differential geometry.

Findings

Characterization of second Ricci solitons on closed and compact manifolds

Analysis of immersed submanifolds as second Ricci solitons

Investigation of second Ricci solitons on warped product manifolds

Abstract

This paper introduce the idea of second Ricci solitons. A second Ricci soliton is nothing but a steady hyperbolic Ricci soliton. We study the geometry of closed and compact second Ricci soliton manifolds. Immersed submanifolds as second solitons also will be investigated. Finally, we investigate this structure on warped product manifolds.