Geometric solitons in a $D$-homothetically deformed Kenmotsu manifold

TL;DR

This paper investigates geometric solitons in a specific class of deformed Kenmotsu manifolds, deriving curvature properties and bounds related to various potential vector fields.

Contribution

It provides explicit formulas for Ricci and scalar curvatures in deformed Kenmotsu manifolds with different potential vector fields and establishes Ricci curvature bounds.

Findings

Explicit Ricci and scalar curvature formulas for deformed Kenmotsu manifolds.

Lower bounds for Ricci curvature in the initial Kenmotsu manifold.

Analysis of solitons with gradient, solenoidal, and Reeb vector fields.

Abstract

We consider almost Riemann and almost Ricci solitons in a $D$-homothetically deformed Kenmotsu manifold having as potential vector field a gradient vector field, a solenoidal vector field or the Reeb vector field of the deformed structure, and explicitly obtain the Ricci and scalar curvatures for some cases. We also provide a lower bound for the Ricci curvature of the initial Kenmotsu manifold when the deformed manifold admits a gradient almost Riemann or almost Ricci soliton.