Pseudo-hyperbolic Gauss maps of Lorentzian surfaces in anti-de Sitter space |
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Authors: | Honoka Kobayashi Naoyuki Koike |
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Institution: | Faculty of Science, Department of Mathematics, Tokyo University of Science, 1-3 Kagurazaka Shinjuku-ku, Tokyo, 162-8601 Japan |
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Abstract: | In this paper, we determine the type numbers of the pseudo-hyperbolic Gauss maps of all oriented Lorentzian surfaces of constant mean and Gaussian curvatures and non-diagonalizable shape operator in the 3-dimensional anti-de Sitter space. Also, we investigate the behavior of type numbers of the pseudo-hyperbolic Gauss map along the parallel family of such oriented Lorentzian surfaces in the 3-dimensional anti-de Sitter space. Furthermore, we investigate the type number of the pseudo-hyperbolic Gauss map of one of Lorentzian hypersurfaces of B-scroll type in a general dimensional anti-de Sitter space. |
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Keywords: | anti-de Sitter space B-scroll complex circle finite type pseudo-hyperbolic Gauss map |
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