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We classify minimal surfaces in $\mathbb S^3$ which are foliated by circles and ruled constant mean curvature (cmc) surfaces in $\mathbb S^3$. First we show that minimal surfaces in $\mathbb S^3$ which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric $\mathbb S^1$-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in $\mathbb S^3$ up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in $\mathbb S^3$ (cf. Theorem 3).
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참고문헌 (5)
참고문헌 신청
U. Dierkes / 2010 / Minimal Surfaces / Springer
Hubert Frank / 1976 / Verallgemeinerte Regelfl�chen / Mathematische Zeitschrift 150(3):261~271
Ryan Hynd / 2009 / Symmetric surfaces of constant mean curvature in 3 / Pacific Journal of Mathematics 241(1):63~115
Nikolai Kutev / 2010 / Minimal surfaces in S 3 foliated by circles / Pacific Journal of Mathematics 248(2):335~354
H. Blaine Lawson / 1970 / Complete Minimal Surfaces in S 3 / The Annals of Mathematics 92(3):335
Hubert Frank / 1976 / Verallgemeinerte Regelfl�chen / Mathematische Zeitschrift 150(3):261~271
Ryan Hynd / 2009 / Symmetric surfaces of constant mean curvature in 3 / Pacific Journal of Mathematics 241(1):63~115
Nikolai Kutev / 2010 / Minimal surfaces in S 3 foliated by circles / Pacific Journal of Mathematics 248(2):335~354
H. Blaine Lawson / 1970 / Complete Minimal Surfaces in S 3 / The Annals of Mathematics 92(3):335
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