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arXiv · 2407.15057

On a metric symplectization of a contact metric manifold

Sannidhi Alape
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Abstract

In this article, we investigate metric structures on the symplectization of a contact metric manifold and prove that there is a unique metric structure, which we call the metric symplectization, for which each slice of the symplectization has a natural induced contact metric structure. We then study the curvature properties of this metric structure and use it to establish equivalent formulations of the $(\kappa, \mu)$-nullity condition in terms of the metric symplectization. We also prove that isomorphisms of the metric symplectizations of $(\kappa, \mu)$-manifolds determine $(\kappa, \mu)$-manifolds up to D-homothetic transformations. These classification results show that the metric symplectization provides a unified framework to classify Sasakian manifolds, K-contact manifolds and $(\kappa, \mu)$-manifolds in terms of their symplectizations.

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Sannidhi Alape. 2024-07-21. On a metric symplectization of a contact metric manifold. https://arxiv.org/abs/2407.15057

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