Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5499928 | Journal of Geometry and Physics | 2017 | 27 Pages |
Abstract
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 âW of W. We study the relationship between pseudohermitian geometry of the strictly pseudoconvex locus M=âWâA and the theory of space-time singularities associated to the Fefferman metric Fθ on the total space of the canonical circle bundle S1âC(M)â¶ÏM. Given any point (0,w0)âA, we show that every lift Î(Ï)âC(M), 0â¤Ïâlog|w0|2<Ïâ2, of the circle Îw0 : r=2cos[log|w0|2âÏ] in M, runs into a curvature singularity of Fefferman's space-time (C(M),Fθ). We show that Σ=Ïâ1(Îw0) is a Lorentzian real surface in (C(M),Fθ) such that the immersion ι:ΣâªC(M) has a flat normal connection. Consequently, there is a natural isometric immersion j:O(Σ)âO(C(M),Σ) between the total spaces of the principal bundles of Lorentzian frames O(1,1)âO(Σ)âΣ and adapted Lorentzian frames O(1,1)ÃO(2)âO(C(M),Σ)âΣ, endowed with Schmidt metrics, descending to a map of bundle completions which maps the b-boundary of Σ into the adapted bundle boundary of C(M), i.e. j(ΣÌ)ââadtC(M).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Elisabetta Barletta, Sorin Dragomir, Marco M. Peloso,