Dept. Math, Hokkaido Univ. EPrints Server

The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat'' spacelike surfaces

Preprint Series # 947
Izumiya, Shyuichi and Saji, Kentaro The mandala of Legendrian dualities for pseudo-spheres in Lorentz-Minkowski space and "flat'' spacelike surfaces. (30 September 2009);

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Abstract

Using the Legnedrian duarities between surfaces in pseudo-spheres in Lorentz-{Minkow}{ski} 4-space, we study various kind of flat surfaces in pseudo-spheres. We consider a surface in the pseudo-sphere and its dual surface. Flatness of a surface is defined by the degeneracy of the dual surface similar to the case for the Gauss map of a flat surface in the Euclidean space. We study singularities of these flat surfaces and dualities of singularities.

Item Type:Preprint
Uncontrolled Keywords:Legendrian duality, Horo-spherical geometry, Horo-flat surfaces, Singularities, Lorentz-Minkowski space, Pseudo-spheres
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:2013