Kodai Mathematical Journal
- Kodai Math. J.
- Volume 28, Number 1 (2005), 146-180.
On Cauchy-Riemann circle bundles
Building on ideas of R. Mizner,  - , and C. Laurent-Thiébaut, , we study the CR geometry of real orientable hypersurfaces of a Sasakian manifold. These are shown to be CR manifolds of CR codimension two and to possess a canonical connection D (parallelizing the maximally complex distribution) similar to the Tanaka-Webster connection (cf. ) in pseudohermitian geometry. Examples arise as circle subbundles , of the Hopf fibration, over a real hypersurface M in the complex projective space. Exploiting the relationship between the second fundamental forms of the immersions N → S2n+1 and M → CPn and a horizontal lifting technique we prove a CR extension theorem for CR functions on N. Under suitable assumptions [, , where a is the Weingarten operator of the immersion N → S2n+1] on the Ricci curvature RicD of D, we show that the first Kohn-Rossi cohomology group of M vanishes. We show that whenever for some , M is a pseudo-Einstein manifold.
Kodai Math. J., Volume 28, Number 1 (2005), 146-180.
First available in Project Euclid: 23 March 2005
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Ciampa, Donato Antonio. On Cauchy-Riemann circle bundles. Kodai Math. J. 28 (2005), no. 1, 146--180. doi:10.2996/kmj/1111588043. https://projecteuclid.org/euclid.kmj/1111588043