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
Downloads: Full-text PDF   Full-text HTML

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd