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On the Degenerate Maximal Spacelike Surfaces

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초록

The purpose of this paper is to investigate various kinds of degeneracy of maximal surfaces in Ln in view of the generalized Gauss map.

Abstract

The purpose of this paper is to investigate various kinds of degeneracy of maximal surfaces in Ln in view of the generalized Gauss map.

참고문헌 (10)

  1. Abe, K., "Indefinite Rigidity of Complex Submanifold and Maximal Sur-faces", Mathematical Proceedings of Cambridge Philosophical Society, 106(3), pp.481~494 (1989)
  2. Akutagawa, K., "The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space", Tohoku Mathematical Journal, 42(1), pp.67~82 (1990)
  3. Asperti, Antonio C., "Spacelike Surfaces in L4 with De-generate Gauss Map", Results in Mathematics, 60(1), pp.185~211 (2011)
  4. Graves, L., "One Isometric Immersions between Lorentz Spaces", Ph.D., pp.1977
  5. 홍성관, "ON THE INDEFINITE POSITIVE QUADRIC Qn-2+", East Asian Mathematical Journal, 32(1), pp.93~100 (2016), 영남수학회[DOI]
  6. 홍성관, "ON THE WEIERSTRASS THEOREM OF A MAXIMAL SPACELIKE SURFACE", East Asian Mathematical Journal, 33(1), pp.115~121 (2017), 영남수학회[DOI]
  7. Kobayasi, O., "Maximal Surfaces in the 3-dimensional Minkowski Space L3", Tokyo J. Math, 6, pp.297~309 (1983)
  8. Milnor, T. K., "Harmonic Maps and Classical Surface Theory in Minkowski 3-space", Trans. of AMS, 280, pp.161~185 (1983)
  9. O'Neil, B., "Semi-Riemannian Geometry" (1983), Academic Press
  10. Osserman, R, "A Survey of Minimal Surfaces" (1986), Dover

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