Solitons of <i>η</i>-Ricci–Bourguignon Type on Submanifolds in (<i>LCS</i>)_<i>m</i> Manifolds

Abstract

In this research article, we concentrate on the exploration of submanifolds in an (LCS)m-manifold B˜. We examine these submanifolds in the context of two distinct vector fields, namely, the characteristic vector field and the concurrent vector field. Initially, we consider some classifications of η-Ricci–Bourguignon (in short, η-RB) solitons on both invariant and anti-invariant submanifolds of B˜ employing the characteristic vector field. We establish several significant findings through this process. Furthermore, we investigate additional results by using η-RB solitons on invariant submanifolds of B˜ with concurrent vector fields, and discuss a supporting example.

Keywords

• <i>η</i>-Ricci–Bourguignon solitons
• (<i>LCS</i>)<i>_m</i>-manifolds
• concurrent vector fields
• <i>η</i>-Einstein manifolds