Abstract
We show that the singularities of spacelike maximal surfaces in Lorentz–Minkowski 3-space generically consist of cuspidal edges, swallowtails and cuspidal cross caps. The same result holds for spacelike mean curvature one surfaces in de Sitter 3-space. To prove these, we shall give a simple criterion for a given singular point on a surface to be a cuspidal cross cap.
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Dedicated to Yusuke Sakane on the occasion of his 60th birthday.
Kentaro Saji was supported by JSPS Research Fellowships for Young Scientists. Masaaki Umehara and Kotaro Yamada were supported by Grant-in-Aid for Scientific Research (No. 15340024(B)) and (No. 14340024(B)), respectively.
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Fujimori, S., Saji, K., Umehara, M. et al. Singularities of maximal surfaces. Math. Z. 259, 827–848 (2008). https://doi.org/10.1007/s00209-007-0250-0
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DOI: https://doi.org/10.1007/s00209-007-0250-0