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Contact Semi-Riemannian Structures in CR Geometry: Some Aspects

Dipartimento di Matematica e Fisica “E. De Giorgi”, Universitá del Salento, Via Provinciale Lecce-Arnesano, 73100 Lecce, Italy
Received: 26 September 2018 / Revised: 20 December 2018 / Accepted: 2 January 2019 / Published: 9 January 2019
(This article belongs to the Special Issue Applications of Differential Geometry)
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Abstract

There is one-to-one correspondence between contact semi-Riemannian structures ( η , ξ , φ , g ) and non-degenerate almost CR structures ( H , ϑ , J ) . In general, a non-degenerate almost CR structure is not a CR structure, that is, in general the integrability condition for H 1 , 0 : = X i J X , X H is not satisfied. In this paper we give a survey on some known results, with the addition of some new results, on the geometry of contact semi-Riemannian manifolds, also in the context of the geometry of Levi non-degenerate almost CR manifolds of hypersurface type, emphasizing similarities and differences with respect to the Riemannian case. View Full-Text
Keywords: contact semi-Riemannian structures; non-degenerate almost CR structures; tangent hyperquadric bundles; homogeneous non-degenerate CR three-manifolds; lie groups; levi-flat CR three-manifolds; bicontact metric structures; levi harmonicity contact semi-Riemannian structures; non-degenerate almost CR structures; tangent hyperquadric bundles; homogeneous non-degenerate CR three-manifolds; lie groups; levi-flat CR three-manifolds; bicontact metric structures; levi harmonicity
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Perrone, D. Contact Semi-Riemannian Structures in CR Geometry: Some Aspects. Axioms 2019, 8, 6.

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