({\kappa},{\mu},\u{psion}=const.)-Contact Metric Manifolds With {\xi}(I_{M})=0

TL;DR

This paper classifies a specific type of contact metric manifold with constant parameters, focusing on those where a certain invariant remains constant along the characteristic vector field, enriching the understanding of their geometric structure.

Contribution

It provides a local classification of ({},{},=const.)-contact metric manifolds with <1 satisfying a specific invariance condition, extending geometric theory.

Findings

Classification of manifolds with constant Boeckx invariant

Characterization of manifolds with <1 under the invariance condition

Insights into the geometric structure of contact metric manifolds

Abstract

We give a local classification of ({\kappa},{\mu},\u{psion}=const.)-contact metric manifold (M,{\phi},{\xi},{\eta},g) with {\kappa}<1 which satisfies the condition" the Boeckx invariant function I_{M}=((1-({\mu}/2))/(\surd(1-{\kappa}))) is constant along the integral curves of the characteristic vector field {\xi}".