In 3D trans-Sasakian manifolds the Newman-Penrose equations encode the structure vector field via spin coefficients and prove that compatible structures on non-space-form E(κ,τ) metrics must be the canonical vertical ones.
Three-Dimensional Almost Contact Metric Manifolds Revisited via the Newman-Penrose Formalism
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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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2026 1verdicts
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Newman--Penrose formalism in $3$-dimensional trans-Sasakian manifolds
In 3D trans-Sasakian manifolds the Newman-Penrose equations encode the structure vector field via spin coefficients and prove that compatible structures on non-space-form E(κ,τ) metrics must be the canonical vertical ones.