Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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MINIMAL AND CONSTANT MEAN CURVATURE SURFACES IN 𝕊3 FOLIATED BY CIRCLES

  • Park, Sung-Ho (Graduate School of Education Hankuk University of Foreign Studies)
  • Received : 2018.12.27
  • Accepted : 2019.05.30
  • Published : 2019.11.30
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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).

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References

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