Dept. Math, Hokkaido Univ. EPrints Server

Legendrian dualities and spacelike hypersurfaces in the lightcone

Preprint Series # 673
Izumiya, Shyuichi Legendrian dualities and spacelike hypersurfaces in the lightcone. (2004);

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Abstract

We show four Legendrian dualities between pseudo-spheres in Minkowski space as a basic theorem. We can apply such dualities for constructing extrinsic differential geometry of spacelike hypersurfaces in pseudo-spheres. In this paper we stick to spacelike hypersurfaces in the lightcone and establish an extrinsic differential geometry which we call the {\it lightcone differential geometry.}

Item Type:Preprint
Uncontrolled Keywords:Legendrian duality, spacelike hypersurfaces, the lightcone, conformally flat Riemannian manifolds
Subjects:53-xx DIFFERENTIAL GEOMETRY
58-xx GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS
ID Code:504