Mapped Null Hypersurfaces and Legendrian Maps

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dc.creatorChernov, Vladimir
dc.date2007-02-11
dc.date.accessioned2026-07-07T10:38:20Z
dc.date.available2026-07-07T10:38:20Z
dc.descriptionFor an $(m+1)$-dimensional space-time $(X^{m+1}, g),$ define a mapped null hypersurface to be a smooth map $ν:N^{m}\to X^{m+1}$ (that is not necessarily an immersion) such that there exists a smooth field of null lines along $ν$ that are both tangent and $g$-orthogonal to $ν.$ We study relations between mapped null hypersurfaces and Legendrian maps to the spherical cotangent bundle $ST^*M$ of an immersed spacelike hypersurface $μ:M^m\to X^{m+1}.$ We show that a Legendrian map $\wt λ: L^{m-1}\to (ST^*M)^{2m-1}$ defines a mapped null hypersurface in $X.$ On the other hand, the intersection of a mapped null hypersurface $ν:N^m\to X^{m+1}$ with an immersed spacelike hypersurface $μ':M'^m\to X^{m+1}$ defines a Legendrian map to the spherical cotangent bundle $ST^*M'.$ This map is a Legendrian immersion if $ν$ came from a Legendrian immersion to $ST^*M$ for some immersed spacelike hypersurface $μ:M^m\to X^{m+1}.$
dc.description13 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0702305
dc.identifierhttp://arxiv.org/abs/math/0702305
dc.identifierJ.Geom.Phys.57:2114-2123,2007
dc.identifierdoi:10.1016/j.geomphys.2007.05.005
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/180684
dc.subjectDifferential Geometry
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectGeometric Topology
dc.subjectSymplectic Geometry
dc.subjectPrimary 53C50; Secondary 57R17
dc.titleMapped Null Hypersurfaces and Legendrian Maps
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