Minimal and Constant mean curvature surfaces in $\mathbb S^3$ foliated by circles
Bull. Korean Math. Soc.
Published online July 26, 2019
Sung-ho Park
Hankuk University of Foreign Studies
Abstract : 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.).
Keywords : minimal surfaces, cmc surfaces, foliation by circles
MSC numbers : 53A10, 53C12
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