Bulletin of the
Korean Mathematical Society BKMS

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