Certain results on Kenmotsu pseudo-metric manifolds

TL;DR

This paper systematically studies Kenmotsu pseudo-metric manifolds, establishing conditions for constant ctional curvature, structure theorems, and analyzing Ricci solitons, revealing their geometric properties and classifications.

Contribution

It provides new necessary and sufficient conditions for constant ctional curvature and characterizes Ricci solitons on Kenmotsu pseudo-metric manifolds.

Findings

Conditions for constant ctional curvature established

Structure theorems for onformally flat manifolds proved

Ricci solitons imply Einstein or constant curvature in specific cases

Abstract

In this paper, a systematic study of Kenmotsu pseudo-metric manifolds are introduced. After studying the properties of this manifolds, we provide necessary and sufficient condition for Kenmotsu pseudo-metric manifold to have constant $\varphi$-sectional curvature, and prove the structure theorem for $\xi$-conformally flat and $\varphi$-conformally flat Kenmotsu pseudo-metric manifolds. Next, we consider Ricci solitons on this manifolds. In particular, we prove that an $\eta$-Einstein Kenmotsu pseudo-metric manifold of dimension higher than 3 admitting a Ricci soliton is Einstein, and a Kenmotsu pseudo-metric 3-manifold admitting a Ricci soliton is of constant curvature $-\varepsilon$.