# 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.
Type de document :
Article dans une revue
Classical and Quantum Gravity, IOP Publishing, 2012, 29 (9), pp.095007

https://hal.archives-ouvertes.fr/hal-00849266
Contributeur : Marc Soret <>
Soumis le : mardi 30 juillet 2013 - 15:10:53
Dernière modification le : samedi 9 juin 2018 - 01:17:17

### Identifiants

• 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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