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arXiv · 2512.22444

Three-Dimensional Almost Contact Metric Manifolds Revisited via the Newman-Penrose Formalism

Satsuki Matsuno
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Abstract

This paper applies the Newman-Penrose formalism-a technique primarily used in General Relativity-to the analysis of three-dimensional almost contact metric (ACM) manifolds. We reformulate and discuss several known notions and properties within the Newman-Penrose framework, demonstrating the applicability of the method in this geometric context. Furthermore, as an application showcasing the utility of the formalism, we address the classification of three-dimensional compact normal ACM manifolds, or equivalently trans-Sasakian manifolds, that admit an $\eta$-Einstein metric.

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Satsuki Matsuno. 2025-12-27. Three-Dimensional Almost Contact Metric Manifolds Revisited via the Newman-Penrose Formalism. https://doi.org/10.1007/s00022-026-00816-6

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