0000000000739898

AUTHOR

Donghe Pei

showing 3 related works from this author

THE HOROSPHERICAL GEOMETRY OF SUBMANIFOLDS IN HYPERBOLIC SPACE

2005

Some geometrical properties associated to the contact of submanifolds with hyperhorospheres in hyperbolic -space are studied as an application of the theory of Legendrian singularities.

Hyperbolic groupGeneral MathematicsHyperbolic spaceMathematical analysisHyperbolic 3-manifoldHyperbolic manifoldUltraparallel theoremGeometryHyperbolic motionMathematics::Geometric TopologyRelatively hyperbolic groupMathematics::Differential GeometryMathematics::Symplectic GeometryHyperbolic triangleMathematicsJournal of the London Mathematical Society
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Umbilicity of space-like submanifolds of Minkowski space

2004

We study some properties of space-like submanifolds in Minkowski n-space, whose points are all umbilic with respect to some normal field. As a consequence of these and some results contained in a paper by Asperti and Dajczer, we obtain that being ν-umbilic with respect to a parallel light-like normal field implies conformal flatness for submanifolds of dimension n − 2 ≥ 3. In the case of surfaces, we relate the umbilicity condition to that of total semi-umbilicity (degeneracy of the curvature ellipse at every point). Moreover, if the considered normal field is parallel, we show that it is everywhere time-like, space-like or light-like if and only if the surface is included in a hyperbolic 3…

PhysicsGeneral MathematicsMinkowski spaceMathematics::Differential GeometrySpace (mathematics)Mathematical physicsHyperboloid modelProceedings of the Royal Society of Edinburgh: Section A Mathematics
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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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