复空间形式中平均曲率梯度长度恒定的哈密顿稳态拉格朗日曲面

中文摘要 AI 辅助

我们研究了复空间形式中平均曲率向量$H$处处非零的哈密顿稳态拉格朗日曲面。我们证明了若高斯曲率为常数且$\grad|H|$具有正的恒定长度，则曲面与周围空间均为平坦的。此外，该浸入局部上等同于由一条柯努螺线与其反射的乘积所得的已知曲面。

英文摘要

We study Hamiltonian stationary Lagrangian surfaces in complex space forms with nowhere-zero mean curvature vector $H$. We prove that if the Gaussian curvature is constant and $\grad|H|$ has positive constant length, then both the surface and the ambient space are flat. Moreover, the immersion is locally congruent to the known surface obtained as the product of a Cornu spiral and its reflection.

发表机构

• Hachinohe Institute of Technology（八户工业大学）

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