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HELICOIDAL SURFACES OF THE THIRD FUNDAMENTAL FORM IN MINKOWSKI 3-SPACE

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초록

We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3- space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

Abstract

We study helicoidal surfaces with the non-degenerate third fundamental form in Minkowski 3-space. In particular, we mainly focus on the study of helicoidal surfaces with light-like axis in Minkowski 3- space. As a result, we classify helicoidal surfaces satisfying an equation in terms of the position vector field and the Laplace operator with respect to the third fundamental form on the surface.

참고문헌 (11)

  1. 최미경, "HELICOIDAL SURFACES AND THEIR GAUSS MAP IN MINKOWSKI 3-SPACE", 대한수학회보, 47(4), pp.859~881 (2010), 대한수학회
  2. 최미경, "Helicoidal surfaces and their Gauss map in Minkowski 3-space II", 대한수학회보, 46(3), pp.567~576 (2009), 대한수학회
  3. M. Choi, "Some classification of surfaces of revolution in Minkowski 3-space", J. Geom, 104(1), pp.85~106 (2013)
  4. O. J. Garay, "An extension of Takahashi’s Theorem", Geom. Dedicata, 34(2), pp.105~112 (1990)
  5. G. Kaimakamis, "Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space satisfying ∆II→r = A→r", J. Geom, 81(1-2), pp.81~92 (2004)
  6. G. Kaimakamis, "Surfaces of revolution in the 3-dimensional Lorentz-Minkowski space E31 satis-fying ∆III→r = A→r", Bull. Greek Math. Soc, 50, pp.75~90 (2005)
  7. O. Kobayashi, "Maximal surfaces in the 3-dimensional Minkowski space L3", Tokyo J. Math, 6(2), pp.297~309 (1983)
  8. C. W. Lee, "Ruled surfaces of non-degenerate third fun-damental forms in Minkowski 3-space", Appl. Math. Comput, 216(11), pp.3200~3208 (2010)
  9. B. O’Neill, "Semi-Riemannian Geometry and its applications to Relativity" (1983), Academic Press
  10. B. Senoussi, "Helicoidal surfaces in the 3-dimensional Lorentz-Minkowski space E31 satisfying ∆III r = Ar", Tsukuba J. Math, 37(2), pp.339~353 (2013)
  11. T. Takahashi, "Minimal immersions of Riemannian manifolds", J. Math. Soc. Japan, 18, pp.380~385 (1966)

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