Contact projective structures. (English) Zbl 1093.53083

Fox, Daniel J. F.

Indiana Univ. Math. J. 54, No. 6, 1547-1598 (2005).

An analogue of the Beltrami theorem is proved for pseudo-Hermitian manifolds with transverse symmetry. Theorem: The contact projective structure induced by an integrable pseudo-Hermitian structure having transverse symmetry is flat if and only if the pseudo-Hermitian structure has constant sectional curvature.

Reviewer: Mihail Banaru (Smolensk)

MSC:

53D10	Contact manifolds (general theory)
53C25	Special Riemannian manifolds (Einstein, Sasakian, etc.)
53B10	Projective connections

Keywords:

contact projective structure; Cartan connection; parabolic geometry; pseudo-Hermitian manifold