Search results for "58C27"

showing 2 items of 2 documents

Singularities of lightlike hypersurfaces in Minkowski four-space

2006

We classify singularities of lightlike hypersurfaces in Minkowski 4-space via the contact invariants for the corresponding spacelike surfaces and lightcones.

Pure mathematicsLightlike hypersurfaceGeneral MathematicsMathematical analysisspacelike surfacelightconePhysics::Classical PhysicsSpace (mathematics)53A3541458C27Computer Science::OtherLorentzian distance-squared functionGeneral Relativity and Quantum CosmologyMinkowski spaceGravitational singularityMathematics::Differential GeometryMathematicsTohoku Mathematical Journal
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The horospherical Gauss-Bonnet type theorem in hyperbolic space

2006

We introduce the notion horospherical curvatures of hypersurfaces in hyperbolic space and show that totally umbilic hypersurfaces with vanishing cur- vatures are only horospheres. We also show that the Gauss-Bonnet type theorem holds for the horospherical Gauss-Kronecker curvature of a closed orientable even dimensional hypersurface in hyperbolic space. + (i1) by using the model in Minkowski space. We introduced the notion of hyperbolic Gauss indicatrices slightly modified the definition of hyperbolic Gauss maps. The notion of hyperbolic indicatrices is independent of the choice of the model of hyperbolic space. Using the hyperbolic Gauss indicatrix, we defined the principal hyperbolic curv…

Pure mathematicsMathematics::Dynamical SystemsGauss-Bonnet type theoremHyperbolic groupMathematics::Complex VariablesGeneral MathematicsHyperbolic spaceMathematical analysisHyperbolic manifoldUltraparallel theoremhorospherical geometryhyperbolic Gauss mapshypersurfacesRelatively hyperbolic groupMathematics::Geometric Topology53A3553A0558C27hyperbolic spaceHyperbolic angleMathematics::Differential GeometryMathematics::Representation TheoryHyperbolic triangleHyperbolic equilibrium pointMathematics
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