Lagrangian surfaces in complex Euclidean plane via spherical and hyperbolic curves
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概要
- 論文の詳細を見る
We present a method to construct a large family of Lagrangian surfaces in complex Euclidean plane $\boldsymbol{C}^2$ by using Legendre curves in the 3-sphere and in the anti de Sitter 3-space or, equivalently, by using spherical and hyperbolic curves, respectively. Among this family, we characterize minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in terms of simple properties of the curvature of the generating curves. As applications, we provide explicitly conformal parametrizations of known and new examples of minimal, constant mean curvature, Hamiltonian-minimal and Willmore surfaces in $\boldsymbol{C}^2$.
- 東北大学の論文
著者
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Chen Bang-yen
Department Of Mathematics Michigan State University
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Castro Ildefonso
Departamento De Matematicas Escuela Politecnica Superior Universidad De Jaen
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Castro Ildefonso
Departamento De Geometria Y Topologia Universidad De Granada
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Chen Bang-Yen
Department of Mathematics, Michigan State University
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