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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 $\rm{SL_2}\mathbb R$ 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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참고문헌 (13)
참고문헌 신청
M. Bekkar / 2007 / Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces / Differ. Geom. Dyn. Syst. 9:21~39
S. Cartier / Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces / arXiv:1303.6391v1
B. Daniel / 2007 / Isometric immersions into 3-dimensional homogeneous manifolds / Comment. Math. Helv. 82(1):87~131
S. Fujimori / 2009 / Spacelike mean curvature one surfaces in de Sitter 3-space / Comm. Anal. Geom. 17(3):383~427
Y. W. Kim / 2009 / Helicoids in ${\mathbb{S}}^2{\times}{\mathbb{R}}$ and ${\mathbb{H}}^2{\times}{\mathbb{R}}$ / Pacific J. Math. 242(2):281~297
S. Cartier / Noether invariants for constant mean curvature surfaces in 3-dimensional homogeneous spaces / arXiv:1303.6391v1
B. Daniel / 2007 / Isometric immersions into 3-dimensional homogeneous manifolds / Comment. Math. Helv. 82(1):87~131
S. Fujimori / 2009 / Spacelike mean curvature one surfaces in de Sitter 3-space / Comm. Anal. Geom. 17(3):383~427
Y. W. Kim / 2009 / Helicoids in
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