# b-Completion of pseudo-Hermitian manifolds

Abstract : We study the interrelation among pseudo-Hermitian and Lorentzian geometry as prompted by the existence of the Fefferman metric. Specifically for any nondegenerate Cauchy-Riemann manifold M we build its b-boundary [$\dot{M}$]. This arises as a S1 quotient of the b-boundary of the (total space of the canonical circle bundle over M endowed with the) Fefferman metric. Points of [$\dot{M}$] are shown to be endpoints of b-incomplete curves. A class of inextensible integral curves of the Reeb vector on a pseudo-Einstein manifold is shown to have an endpoint on the b-boundary provided that the horizontal gradient of the pseudo-Hermitian scalar curvature satisfies an appropriate boundedness condition.

https://hal.archives-ouvertes.fr/hal-00849266
Contributor : Marc Soret <>
Submitted on : Tuesday, July 30, 2013 - 3:10:53 PM
Last modification on : Friday, August 9, 2019 - 3:24:03 PM

### Identifiers

• HAL Id : hal-00849266, version 1

### Citation

Marc Soret, Sorin Dragomir, Elisabetta Barletta, Howard Jacobowitz, Marc Soret, et al.. b-Completion of pseudo-Hermitian manifolds. Classical and Quantum Gravity, IOP Publishing, 2012, 29 (9), pp.095007. ⟨hal-00849266⟩

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