대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제32권1호
  • /
  • Pages.147-163
  • /
  • 2017
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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FOCAL SURFACES AND EVOLUTES OF CURVES IN HYPERBOLIC SPACE

  • 투고 : 2016.02.05
  • 발행 : 2017.01.31
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초록

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.

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참고문헌

  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