Ricci-like solitons with arbitrary potential and gradient almost Ricci-like solitons on Sasaki-like almost contact B-metric manifolds

TL;DR

This paper introduces and analyzes Ricci-like solitons with arbitrary potential on Sasaki-like almost contact B-metric manifolds, revealing their Ricci tensor structure and providing explicit Lie group examples.

Contribution

It defines Ricci-like solitons with arbitrary potential on Sasaki-like manifolds and characterizes their Ricci tensor and soliton coefficients, with explicit low-dimensional examples.

Findings

Ricci tensor is the vertical component of B-metrics multiplied by a constant

Gradient almost Ricci-like solitons have constant soliton coefficients

Explicit Lie group examples in dimensions 3 and 5

Abstract

Ricci-like solitons with arbitrary potential are introduced and studied on Sasaki-like almost contact B-metric manifolds. It is proved that the Ricci tensor of such a soliton is the vertical component of both B-metrics multiplied by a constant. It is established that gradient almost Ricci-like solitons have constant soliton coefficients. Explicit examples of Lie groups as manifolds of dimensions 3 and 5 equipped with the structures studied are provided.