Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HELICOIDAL KILLING FIELDS, HELICOIDS AND RULED MINIMAL SURFACES IN HOMOGENEOUS THREE-MANIFOLDS

  • Received : 2017.10.20
  • Accepted : 2018.04.09
  • Published : 2018.09.01
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Abstract

We provide definitions for the helicoidal Killing field and the helicoid in arbitrary three-manifolds, and investigate helicoids and ruled minimal surfaces in homogeneous three-manifolds, mainly in $SL_2{\mathbb{R}}$ and Sol(3). In so doing we finish our classification of ruled minimal surfaces in homogeneous three-manifolds with the isometry group of dimension 4.

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References

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