Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 58, Number 3 (2014), 807-846.
Riemannian almost CR manifolds with torsion
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).
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
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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. https://projecteuclid.org/euclid.ijm/1441790391