CIRCLE-FOLIATED MINIMAL SURFACES IN 4-DIMENSIONAL SPACE FORMS
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초록
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.
Abstract
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.
참고문헌 (7)
- M. Abramowitz, "Handbook of mathematical functions with formulas, graphs, and mathematical tables" (1964), Government Printing Office
- A. Enneper, "Die cyklischen fl¨achen", Z. Math Phys, 14, pp.393~421 (1869)
- H. Frank, "Verallgemeinerte Regelfl¨achen", Math. Z, 150(3), pp.261~271 (1976)
- D. Hoffman, "The geometry of the generalized Gauss map", Mem. Amer. Math. Soc, 28(236), pp.105~ (1980)
- R. Hynd, "Symmetric surfaces of constant mean curvature in S3", Pacific J. Math, 241(1), pp.63~115 (2009)
- H. Lawson, "Complete minimal surfaces in S3", Ann. Math, 92(3), pp.335~374 (1970)
- J. Nitsche, "Lectures on Minimal Surfaces" (1989), Cambridge Univ. Press