The curvature tensor of almost cosymplectic and almost Kenmotsu (\kappa,\mu,\nu)-spaces

TL;DR

This paper investigates the Riemann curvature tensor of (,,)-spaces with almost cosymplectic and almost Kenmotsu structures, introducing a generalization of contact metric spaces and providing examples and obstructions.

Contribution

It explicitly characterizes the curvature tensor for these spaces and defines a new generalized class of (,,)-spaces, expanding the understanding of their geometric properties.

Findings

Explicit formulas for the curvature tensor in these structures

Introduction of a natural generalization of contact metric (,,)-spaces

Examples and obstructions for the existence of these spaces

Abstract

We study the Riemann curvature tensor of (\kappa,\mu,\nu)-spaces when they have almost cosymplectic and almost Kenmotsu structures, giving its writing explicitly. This leads to the definition and study of a natural generalisation of the contact metric (\kappa,\mu,\nu)-spaces. We present examples or obstruction results of these spaces in all possible cases.