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Singular 4-Webs of Asymptotic Lines of Spacelike Surfaces in de Sitter 5-space

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Abstract

In this paper, we continue the study of the geometry of spacelike surfaces in de Sitter 5-space. We define invariants of the second fundamental form and consider their geometrical properties. We also investigate generic properties of the surfaces defined as solutions of the equations of asymptotic directions (AD) and lightlike binormal directions (BD) of spacelike surfaces.

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Author information

Correspondence to Ana Claudia Nabarro.

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M. Kasedou work was supported by JSPS KAKENHI Grant Number JP15K17548. A. C. Nabarro is supported by FAPESP Grant 2016/19139-7. M. A. S. Ruas is partially supported by CNPq Grant 306306/2015–8 and FAPESP Grant 2014/00304–2.

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Kasedou, M., Nabarro, A.C. & Ruas, M.A.S. Singular 4-Webs of Asymptotic Lines of Spacelike Surfaces in de Sitter 5-space. Bull Braz Math Soc, New Series 51, 293–315 (2020). https://doi.org/10.1007/s00574-019-00153-0

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Keywords

  • Spacelike surface
  • de Sitter 5-space
  • Second order geometry
  • Asymptotic directions (AD)
  • Lightlike binormal directions
  • 4-Web binary differential equations and their discriminants
  • Non isolated singularities of AD-equations

Mathematics Subject Classification

  • 53A35
  • 53B30
  • 58K05