D-homothetically fixed, weakly $(\kappa, \mu)$-structures on contact metric spaces

TL;DR

This paper introduces a weak $(ppa ,mu)$-structure on contact metric spaces, extending known results from Sasakian geometry to a broader class with weaker conditions, and explores their existence under certain invariants.

Contribution

It defines a new weak $(ppa ,mu)$-structure, generalizing K-contact spaces, and demonstrates that many properties of Sasakian spaces persist in this broader setting.

Findings

Existence of K-contact structures under specific conditions.

Existence of $(ppa ,mu=2)$-structures with certain invariants.

Many classical results extend to the weak generalized setting.

Abstract

Contact metric $(\kappa ,\mu )$-spaces are generalizations of Sasakian spaces. We introduce a weak $(\kappa ,\mu )$ condition as a generalization of the K-contact one and show that many of the known results from generalized Sasakian geometry hold in the weaker generalized K-contact geometry setting. In particular, we prove existence of K-contact and $(\kappa ,\mu =2)$-structures under some conditions on the Boeckx invariant.