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# Lightlike developables in Minkowski 3-space

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 Title: Lightlike developables in Minkowski 3-space Authors: CHINO, Sachiko Browse this author IZUMIYA, Shyuichi Browse this author Keywords: Lightlike developables Minkowski $3$-space singularities Issue Date: 7-Apr-2006 Publisher: Department of Mathematics, Hokkaido University Journal Title: Hokkaido University Preprint Series in Mathematics Volume: 781 Start Page: 1 End Page: 11 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. Type: bulletin (article) URI: http://hdl.handle.net/2115/69589 Appears in Collections: 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics