Flat lightlike hypersurfaces in Lorentz-Minkowski 4-space. (English) Zbl 1188.53056
The authors deal with the flat light-like hypersurfaces in Lorentz-Minkowski 4-spaces, with specific attention to the study of their singilarities in which a classification has been given. They prove that the generic singularities are the suspended cuspidal edge, the suspended swallowtail, the suspended cuspidal cross cap and the \(A_{4}\)-type hypersurface singularity. The authors also observe that the suspended cuspidal cross cap does not appear as a generic singularity in the general case of light-like hypersurfaces. Finally, they end the paper by classifying generic singularities of flat space-like surfaces with partially parallel normal frame.
Reviewer: Fortuné Massamba (Gaborone)
MSC:
| 53C40 | Global submanifolds |
| 58K05 | Critical points of functions and mappings on manifolds |
| 53A35 | Non-Euclidean differential geometry |
Keywords:
flat lightlike hypersurface; lightlike flat spacelike surface; Lorentz-Minkowski space; Legendrian singularitiesReferences:
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