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July 2021 Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint
Atsufumi Honda, Shyuichi Izumiya, Kentaro Saji, Keisuke Teramoto
Tsukuba J. Math. 45(1): 51-68 (July 2021). DOI: 10.21099/tkbjm/20214501051

Abstract

A surface in the Lorentz-Minkowski 3-space is generally a mixed type surface, namely, it has the lightlike locus. We study local differential geometric properties of such a locus on a mixed type surface. We define a frame field along a lightlike locus, and using it, we define two lightlike ruled surfaces along a lightlike locus which can be regarded as lightlike approximations of the surface along the lightlike locus. We study a relationship of singularities of these lightlike surfaces and differential geometric properties of the lightlike locus. We also consider the intersection curve of two lightlike approximations, which gives a model curve of the lightlike locus.

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Atsufumi Honda. Shyuichi Izumiya. Kentaro Saji. Keisuke Teramoto. "Geometry of lightlike locus on mixed type surfaces in Lorentz-Minkowski 3-space from a contact viewpoint." Tsukuba J. Math. 45 (1) 51 - 68, July 2021. https://doi.org/10.21099/tkbjm/20214501051

Information

Published: July 2021
First available in Project Euclid: 29 October 2021

Digital Object Identifier: 10.21099/tkbjm/20214501051

Subjects:
Primary: 53B30
Secondary: 53A55 , 57R45 , 58K05

Keywords: curves on surfaces , Darboux frame , flat approximations , mixed type surfaces

Rights: Copyright © 2021 University of Tsukuba, Institute of Mathematics

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Vol.45 • No. 1 • July 2021
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