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Keywords = homogeneous non-degenerate CR three-manifolds

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50 pages, 598 KiB  
Review
Contact Semi-Riemannian Structures in CR Geometry: Some Aspects
by Domenico Perrone
Axioms 2019, 8(1), 6; https://doi.org/10.3390/axioms8010006 - 9 Jan 2019
Cited by 11 | Viewed by 4461
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Applications of Differential Geometry)
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