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FOCAL SURFACES AND EVOLUTES OF CURVES IN HYPERBOLIC SPACE

  • Hayashi, Ryota ;
  • Izumiya, Shyuichi ;
  • Sato, Takami
  • Received : 2016.02.05
  • Published : 2017.01.31

Abstract

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.

Keywords

hyperbolic space;hyperbolic space curves;focal surfaces;evolutes

References

  1. J. W. Bruce and P. J. Giblin, Curves and Singularities, Second Edition, Cambridge University press, 1992.
  2. S. Izumiya, D.-H. Pei, and T. Sano, Horospherical surfaces of curves in hyperbolic space, Publ. Math. Debrecen 64 (2004), no. 1-2, 1-13.
  3. S. Izumiya and T. Sato, Lightlike hypersurfaces along spacelike submanifolds in Minkowski space-time, J. Geom. Phys. 71 (2013), 30-52. https://doi.org/10.1016/j.geomphys.2013.03.005