二维复空间形式中具有常高斯曲率的双调和拉格朗日曲面
Biharmonic Lagrangian surfaces with constant Gaussian curvature in $2$-dimensional complex space forms
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中文总结 AI 辅助
本文在二维复空间形式中完整分类了具有常高斯曲率的双调和拉格朗日曲面，并由此分类了平坦法丛情形，证明了伪脐双调和拉格朗日曲面必为极小曲面。
中文摘要 AI 辅助
常曲率是子流形几何中最基本的内部条件之一。在内部曲率约束下研究双调和子流形的存在性与分类通常较为困难，因为双调和方程是用外部数据表示的。本文给出了二维复空间形式中具有常高斯曲率的双调和拉格朗日曲面的完整分类。作为推论，我们分类了具有平坦法丛的双调和拉格朗日曲面，并证明了伪脐双调和拉格朗日曲面必然是极小的。
英文摘要
Constant curvature is one of the most fundamental intrinsic conditions in submanifold geometry. Investigating the existence and classification of biharmonic submanifolds under intrinsic curvature constraints is generally difficult, since the biharmonic equation is expressed in terms of extrinsic data. In this paper, we obtain a complete classification of biharmonic Lagrangian surfaces with constant Gaussian curvature in 2-dimensional complex space forms. As a consequence, we classify the biharmonic Lagrangian surfaces with flat normal bundle and we prove that pseudo-umbilical biharmonic Lagrangian surfaces are necessarily minimal.
发表机构
- Dongbei University of Finance and Economics（东北财经大学）
- Al.I. Cuza University of Iasi（雅西亚历山德鲁·伊万库扎大学）
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