Contact Pseudo-Metric Manifolds of Constant Curvature and CR Geometry

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• 作者：Domenico Perrone
• 关键词：53D10 ; 53C50 ; 53C15 ; Contact pseudo ; metric structures ; pseudo ; Riemannian metrics ; sectional curvature ; non ; degenerate CR structure ; pseudohermitian torsion
• 刊名：Results in Mathematics
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：66
• 期：1-2
• 页码：213-225
• 全文大小：225 KB
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• 作者单位：Domenico Perrone (1)
  
  1. Dipartimento di Matematica e Fisica “E. De Giorgi- Università del Salento, Lecce, Italy
  
• ISSN：1420-9012

文摘

In this paper, we show that if an integrable contact pseudo-metric manifold of dimension 2n?+?1, n??2, has constant sectional curvature \({\kappa}\) , then the structure is Sasakian and \({\kappa=\varepsilon=g(\xi,\xi)}\) , where \({\xi}\) is the Reeb vector field. We note that the notion of contact pseudo-metric structure is equivalent to the notion of non-degenerate almost CR manifold, then an equivalent statement of this result holds in terms of CR geometry. Moreover, we study the pseudohermitian torsion \({\tau}\) of a non-degenerate almost CR manifold.