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Title: Partially Integrable Almost CR Manifolds of CR Dimension and Codimension Two
Contributor(s): Cap, A (author); Schmalz, G (author)orcid 
Publication Date: 2002
Open Access: Yes
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Abstract: We extend the results of [11] on embedded CR manifolds of CR dimension and codimension two to abstract partially integrable almost CR manifolds. We prove that points on such manifolds fall into three different classes, two of which (the hyperbolic and the elliptic points) always make up open seats. We prove that manifolds consisting entirely of hyperbolic (respectively elliptic) points admit canonical Cartan connections. More precisely, these structures are shown to be exactly the normal parabolic geometries of types (PSU(2,1) x PSU(2,1),B x B), respectively (PSL(3,C),B), where B indicates a Borel subgroup. We then show how general tools for parabolic geometries can be used to obtain geometric interpretations of the torsion part of the harmonic components of the curvature of the Cartan connection in the elliptic case.
Publication Type: Book Chapter
Source of Publication: Lie groups, geometric structures, and differential equations: one hundred years after Sophus Lie, p. 45-77
Publisher: Mathematical Society of Japan
Place of Publication: Japan
ISBN: 4931469213
Field of Research (FOR): 010102 Algebraic and Differential Geometry
HERDC Category Description: B1 Chapter in a Scholarly Book
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Series Name: Advanced Studies in Pure Mathematics
Series Number : 37
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Appears in Collections:Book Chapter

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