Minimal and Constant mean curvature surfaces in $\mathbb S^3$ foliated by circles
Bull. Korean Math. Soc. 2019 Vol. 56, No. 6, 1539-1550 https://doi.org/10.4134/BKMS.b181266 Published online July 26, 2019 Printed November 30, 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 and cmc surfaces, circle foliation
MSC numbers : 53A10, 53C12
Supported by : This work was supported by Hankuk University of Foreign Studies Research Fund
