Natural almost contact structures and their 3D homogeneous models |
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| Authors: | Giovanni Calvaruso Antonella Perrone |
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| Affiliation: | Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Lecce, Italy |
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| Abstract: | We consider a natural condition determining a large class of almost contact metric structures. We study their geometry, emphasizing that this class shares several properties with contact metric manifolds. We then give a complete classification of left‐invariant examples on three‐dimensional Lie groups, and show that any simply connected homogeneous Riemannian three‐manifold  admits a natural almost contact structure having g as a compatible metric. Moreover, we investigate left‐invariant CR structures corresponding to natural almost contact metric structures. |
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| Keywords: | Almost contact metric structures normal structures CR structures homogeneous Riemannian three‐manifolds Riemannian Lie groups 53C15 53C30 53D15 22E15 |
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