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Catenoid and Riemann’s minimal surface are foliated by circles, that is, they are union of circles. In R3, there is no other nonplanar example of circle-foliated minimal surfaces. In R4, the graph Gc of w = c/z for real constant c and ζ ∈ C＼{0} is also foliated by circles. In this paper, we show that every circle-foliated minimal surface in Rn is either a catenoid or Riemann’s minimal surface in some 3-dimensional Affine subspace or a graph surface Gc in some 4-dimensional Affine subspace.
We use the property that Gc is circle-foliated to construct circle-foliated minimal surfaces in S4 and H4.
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참고문헌 (7)
참고문헌 신청
A. Enneper / 1869 / Die cyklischen fl¨achen / Z. Math Phys 14 : 393 ~ 421
D. Hoffman / 1980 / The geometry of the generalized Gauss map / Mem. Amer. Math. Soc 28 (236) : 105 ~
H. Frank / 1976 / Verallgemeinerte Regelfl¨achen / Math. Z 150 (3) : 261 ~ 271
H. Lawson / 1970 / Complete minimal surfaces in S3 / Ann. Math 92 (3) : 335 ~ 374
J. Nitsche / 1989 / Lectures on Minimal Surfaces / Cambridge Univ. Press
D. Hoffman / 1980 / The geometry of the generalized Gauss map / Mem. Amer. Math. Soc 28 (236) : 105 ~
H. Frank / 1976 / Verallgemeinerte Regelfl¨achen / Math. Z 150 (3) : 261 ~ 271
H. Lawson / 1970 / Complete minimal surfaces in S3 / Ann. Math 92 (3) : 335 ~ 374
J. Nitsche / 1989 / Lectures on Minimal Surfaces / Cambridge Univ. Press
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