Natural almost contact structures and their 3D homogeneous models

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• 作者：Giovanni Calvaruso and Antonella Perrone
• 刊名：Mathematische Nachrichten
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：289
• 期：11-12
• 页码：1370-1385
• 全文大小：235K
• ISSN：1522-2616

文摘

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 (M,g) 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.