A note on $LP$-Kenmotsu manifolds admitting Ricci-Yamabe solitons

TL;DR

This paper investigates Lorentzian para-Kenmotsu manifolds that admit Ricci-Yamabe solitons, providing theoretical insights and a concrete 5-dimensional example to illustrate the findings.

Contribution

It characterizes Ricci-Yamabe solitons on $LP$-Kenmotsu manifolds and constructs a specific example demonstrating the existence of such structures.

Findings

Existence of Ricci-Yamabe solitons on $LP$-Kenmotsu manifolds

Construction of a 5-dimensional non-trivial example

Insights into geometric properties of these manifolds

Abstract

In the current note, we study Lorentzian para-Kenmotsu (in brief, $LP$-Kenmotsu) manifolds admitting Ricci-Yamabe solitons (RYS) and gradient Ricci-Yamabe soliton (gradient RYS). At last by constructing a 5-dimensional non-trivial example we illustrate our result.