Worm domains and Fefferman space–time singularities

Let W be a smoothly bounded worm domain in C2 and let A=Null(Lθ) be the set of Levi-flat points on the boundary ∂W of W. We study the relationship between pseudohermitian geometry of the strictly pseudoconvex locus M=∂W∖A and the theory of space–time singularities associated to the Fefferman metric...

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Bibliographic Details
Published in:Journal of geometry and physics 2017-10, Vol.120, p.142-168
Main Authors: Barletta, Elisabetta, Dragomir, Sorin, Peloso, Marco M.
Format: Article
Language:English
Subjects:
Bundle boundary
Curvature singularity
Fefferman’s metric
Levi form
Schmidt metric
Worm domain
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Summary:Let W be a smoothly bounded worm domain in C2 and let A=Null(Lθ) be the set of Levi-flat points on the boundary ∂W of W. We study the relationship between pseudohermitian geometry of the strictly pseudoconvex locus M=∂W∖A and the theory of space–time singularities associated to the Fefferman metric Fθ on the total space of the canonical circle bundle S1→C(M)⟶πM. Given any point (0,w0)∈A, we show that every lift Γ(φ)∈C(M), 0≤φ−log|w0|2
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2017.06.001