Illinois Journal of Mathematics

Riemannian almost CR manifolds with torsion

Giulia Dileo and Antonio Lotta

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We characterize and study Riemannian almost CR manifolds admitting characteristic connections, that is, metric connections with totally skew-symmetric torsion parallelizing the almost CR structure. Natural constructions are provided of new nontrivial examples. We study the influence of the curvature of the metric on the underlying almost CR structure. A global classification is obtained under flatness assumption of a characteristic connection, provided that the fundamental $2$-form of the structure is closed (quasi Sasakian condition).

Article information

Illinois J. Math., Volume 58, Number 3 (2014), 807-846.

Received: 15 July 2014
Revised: 19 February 2015
First available in Project Euclid: 9 September 2015

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Zentralblatt MATH identifier

Primary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.)
Secondary: 53B05: Linear and affine connections


Dileo, Giulia; Lotta, Antonio. Riemannian almost CR manifolds with torsion. Illinois J. Math. 58 (2014), no. 3, 807--846. doi:10.1215/ijm/1441790391.

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