MINIMAL AND CONSTANT MEAN CURVATURE SURFACES IN 3 FOLIATED BY CIRCLES

Abstract

We classify minimal surfaces in S3 which are foliated by circles and ruled constant mean curvature (cmc) surfaces in S3. First we show that minimal surfaces in S3 which are foliated by circles are either ruled (that is, foliated by geodesics) or rotationally symmetric (that is, invariant under an isometric S1-action which fixes a geodesic). Secondly, we show that, locally, there is only one ruled cmc surface in S3 up to isometry for each nonnegative mean curvature. We give a parametrization of the ruled cmc surface in S3 (cf. Theorem 3).