Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds

TL;DR

This paper introduces a weak analogue of quasi contact metric manifolds, generalizing known theorems and establishing new criteria for K-contact and Sasakian manifolds based on curvature and geometric conditions.

Contribution

It defines weak quasi contact metric manifolds and extends classical results, providing novel characterizations of K-contact and Sasakian manifolds.

Findings

Generalized classical theorems to weak quasi contact structures

Provided new curvature-based criteria for K-contact manifolds

Established conditions characterizing Sasakian manifolds

Abstract

Quasi contact metric manifolds (introduced by Y. Tashiro and then studied by several authors) are a natural extension of the contact metric manifolds. Weak almost contact metric manifolds, i.e., the linear complex structure on the contact distribution is replaced by a nonsingular skew-symmetric tensor, were defined by the author and R. Wolak. In this paper, we study a weak analogue of quasi contact metric manifolds. Our main results generalize some well known theorems and provide new criterions for K-contact and Sasakian manifolds in terms of conditions on the curvature tensor and other geometric objects associated with the weak quasi-contact metric structure.