East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
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ON THE DEGENERATE MAXIMAL SURFACES IN ��4

  • Received : 2021.01.06
  • Accepted : 2021.01.25
  • Published : 2021.01.31
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Abstract

The purpose of this paper is to investigate various kinds of degeneracy of maximal surfaces in ��4 in view of the generalized Gauss map.

Keywords

References

  1. Abe, K. and Magid, M., Indefinite Rigidity of Complex Submanifold and Maximal Surfaces, Mathematical Proceedings of Cambridge Philosophical Society 106 (1989), no. 3, 481-494 https://doi.org/10.1017/S0305004100068225
  2. Akutagawa, K. and Nishigawa, S., The Gauss Map and Spacelike Surfaces with Prescribed Mean Curvature in Minkowski 3-Space, Tohoku Mathematical Journal 42 (1990), no. 1, 67-82. https://doi.org/10.2748/tmj/1178227694
  3. Asperti, Antonio C. and Vilhena, Jose Antonio M., Spacelike Surfaces in L4 with Degenerate Gauss Map, Results in Mathematics 60 (2011), no. 1, 185-211. https://doi.org/10.1007/s00025-011-0146-5
  4. Graves, L., Codimension One Isometric Immersions between Lorentz Spaces, Ph.D. Thesis, Brown University, 1977.
  5. Hong, SK., On the Indefinite Quadric ℚn-2+, East Asian Math. Journal 32 (2016), no. 1, 93-100. https://doi.org/10.7858/eamj.2016.010
  6. Hong, SK., On the Degenerate Maximal Spacelike Surfaces, East Asian Math. Journal 35 (2019), no. 1, 109-115. https://doi.org/10.7858/EAMJ.2019.014
  7. Kobayasi, O., Maximal Surfaces in the 3-dimensional Minkowski Space L3, Tokyo J. Math. 6 (1983), 297-309.
  8. Milnor, T. K., Harmonic Maps and Classical Surface Theory in Minkowski 3-space, Trans. of AMS 280 (1983), 161-185. https://doi.org/10.1090/S0002-9947-1983-0712254-7
  9. O'Neil, B., Semi-Riemannian Geometry, Academic Press, New York, 1983.
  10. Osserman, R., A Survey of Minimal Surfaces, Dover, New York, 1986