Dept. Math, Hokkaido Univ. EPrints Server

Lightlike developables in Minkowski 3-space

Preprint Series # 781
CHINO, Sachiko and IZUMIYA, Shyuichi Lightlike developables in Minkowski 3-space. (2006);

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Abstract

We say that a surface in Minkowski $3$-space is a {\it lightlike developable} if any pseudo-normal vector of the regular part of the surface is lightlike. We show that such a surface is a part of a lightlike plane, the lightcone, the tangent surface of a spacelike curve in a lightlike plane, the tangent surface of a lightlike curve or the glue of such surfaces. The most interesting surfaces in such the class of surfaces is the tangent surface of a lightlike curve. We give a classification of the singularities for the tangent surface of a generic lightlike curve. As a consequence, the $H_3$ type singularity appears in generic.

Item Type:Preprint
Additional Information:50
Uncontrolled Keywords:Lightlike developables, Minkowski $3$-space, singularities
Subjects:53-xx DIFFERENTIAL GEOMETRY
ID Code:1524