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Singularities of Anti de Sitter torus Gauss maps

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Abstract

We study timelike surfaces in Anti de Sitter 3-space as an application of singularity theory. We define two mappings associated to a timelike surface which are called Anti de Sitter nullcone Gauss image and Anti de Sitter torus Gauss map. We also define a family of functions named Anti de Sitter null height function on the timelike surface. We use this family of functions as a basic tool to investigate the geometric meanings of singularities of the Anti de Sitter nullcone Gauss image and the Anti de Sitter torus Gauss map.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P.R. China

    Liang Chen

  2. Department of Mathematics Faculty of Science, Hokkaido University, Sapporo, 060-0810, Japan

    Shyuichi Izumiya

Authors
  1. Liang Chen
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  2. Shyuichi Izumiya
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Corresponding author

Correspondence to Liang Chen.

Additional information

Partially supported by Science Foundation for Young Teachers of Northeast Normal University No. 20070105 and the State Scholarship Fund of CSC No. 20073021, China.

Partially supported by Grant-in Aid for Scientific Research No. 18654007 and No. 18340013.

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Chen, L., Izumiya, S. Singularities of Anti de Sitter torus Gauss maps. Bull Braz Math Soc, New Series 41, 37–61 (2010). https://doi.org/10.1007/s00574-010-0002-3

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  • DOI: https://doi.org/10.1007/s00574-010-0002-3

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