Cap, A

Schmalz, G

2002

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 (<i>PSU</i>(2,1) x <i>PSU</i>(2,1),<i>B</i> x <i>B</i>), respectively (<i>PSL</i>(3,C),<i>B</i>), where <i>B</i> 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.

Lie groups, geometric structures, and differential equations: one hundred years after Sophus Lie, p. 45-77

4931469213

https://hdl.handle.net/1959.11/977

Mathematical Society of Japan

Advanced Studies in Pure Mathematics

1

Partially Integrable Almost CR Manifolds of CR Dimension and Codimension Two

Book Chapter

Publication