Young‐Wook Kim, Sung-Eun Koh, H. Lee, Heayong Shin, Seong-Deog Yang
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Helicoidal killing fields, helicoids and ruled minimal surfaces in homogeneous three-manifolds
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 SL2R 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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