A new construction of Lagrangians in the complex Euclidean plane in terms of planar curves

作者：Castro Ildefonso^*; Lerma Ana M

来源：Journal of Geometry and Physics, 2014, 75: 162-172.

DOI：10.1016/j.geomphys.2013.10.002

• Lagrangian surfaces
• Minimal surfaces
• CMC surfaces
• Hamiltonian stationary surfaces
• Mean curvature flow solitons
• Willmore surfaces

We introduce a new method to construct a large family of Lagrangian surfaces in complex Euclidean plane C-2 by means of two planar curves making use of their usual product as complex functions and integrating the Hermitian product of their position and tangent vectors. %26lt;br%26gt;Among this family, we characterize minimal, constant mean curvature, Hamiltonian stationary, solitons for mean curvature flow and Will more surfaces in terms of simple properties of the curvatures of the generating curves. As an application, we provide explicitly conformal parametrizations of known and new examples of these classes of Lagrangians in C-2.

• 出版日期2014-1