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arXiv · 2410.02752

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

Vladimir Rovenski
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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.

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Vladimir Rovenski. 2024-10-03. Weak quasi contact metric manifolds and new characteristics of K-contact and Sasakian manifolds. https://arxiv.org/abs/2410.02752

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