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Article Dans Une Revue Classical and Quantum Gravity Année : 2012

b-Completion of pseudo-Hermitian manifolds

Résumé

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.
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Dates et versions

hal-00849266 , version 1 (30-07-2013)

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  • HAL Id : hal-00849266 , version 1

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