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The research aims to explore contact metric structures on three-dimensional manifolds with a focus on specific geometric properties.

April 1, 2026Open Access

Contact metric structures with the typical contact form on the 3-dimensional manifold

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The research aims to explore contact metric structures on three-dimensional manifolds with a focus on specific geometric properties.
Identified the typical contact form on manifolds such as S³, R³, and T³.
Analyzed contact metric structures (φ, ξ, η, g) on the aforementioned manifolds.
Classified the structures based on conditions like η-Einstein, Sasakian, and K-contact.
Established clear definitions of contact metric structures for S³, R³, and T³.
Identified conditions under which the metric structures exhibit η-Einstein properties.
Differentiated among Sasakian and K-contact structures within the context of these manifolds.

Implication

Analysis identifies contact metric structures in 3D manifolds, indicating various geometric characteristics.

Abstract

Let η be a typical contact form on the manifold M³ = S³, R³ and T³. We determine contact metric structures (φ, ξ, η, g) on M³. And then we consider the cases that (φ, ξ, η, g) is η-Einstein, or it is Sasakian, or it is K-contact, respectively.

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Cite This Study

Akio YAMAMOTO (2020) studied this question.

synapsesocial.com/papers/69cd7b065652765b073a8b56 https://doi.org/10.15099/00020837

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Implication

Analysis identifies contact metric structures in 3D manifolds, indicating various geometric characteristics.

Contact metric structures with the typical contact form on the 3-dimensional manifold

Key Points

Implication

Abstract

Discussion

Cite This Study

Contact metric structures with the typical contact form on the 3-dimensional manifold

Key Points

Implication

Abstract

Discussion

Cite This Study

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