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Dualities of Differential Geometric Invariants on Cuspidal Edges on Flat Fronts in the Hyperbolic Space and the de Sitter Space

Abstract

We compute the differential geometric invariants of cuspidal edges on flat surfaces in hyperbolic 3-space and in de Sitter space. Several dualities of invariants are pointed out.

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Acknowledgements

The authors would like to thank Masaaki Umehara for valuable comments, and thank Shun Iguchi and Mao Nomura for helping calculations. They also thank the referee for helpful comments.

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Correspondence to Keisuke Teramoto.

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The first author was partly supported by the JSPS KAKENHI Grant Number 18K03301 and the second author by the JSPS KAKENHI Grant Number 17J02151.

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Saji, K., Teramoto, K. Dualities of Differential Geometric Invariants on Cuspidal Edges on Flat Fronts in the Hyperbolic Space and the de Sitter Space. Mediterr. J. Math. 17, 42 (2020). https://doi.org/10.1007/s00009-020-1474-z

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Keywords

  • Cuspidal edge
  • flat front
  • duality

Mathematics Subject Classification

  • Primary 53A55
  • Secondary 53A35
  • 57R45