A class of non-compact homogeneous Lagrangian submanifolds in complex hyperbolic spaces

详细信息    查看全文

• 作者：Takahiro Hashinaga ; Toru Kajigaya
• 关键词：Homogeneous Lagrangian submanifolds ; Complex hyperbolic spaces
• 刊名：Annals of Global Analysis and Geometry
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：51
• 期：1
• 页码：21-33
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Statistics for Business/Economics/Mathematical Finance/Insurance; Theoretical, Mathematical and Computational Physics; Group Theory and Generalizations; Geometry;
• 出版者：Springer Netherlands
• ISSN：1572-9060
• 卷排序：51

文摘

We study homogeneous Lagrangian submanifolds in complex hyperbolic spaces. We show there exists a correspondence between compact homogeneous Lagrangian submanifolds in \(\mathbb {C}H^{n}\) and the ones in \(\mathbb {C}^n\), or equivalently, in \(\mathbb {C}P^{n-1}\). Furthermore, we construct and classify non-compact homogeneous Lagrangian submanifolds in \(\mathbb {C}H^n\) obtained by the actions of connected closed subgroups of the solvable part of the Iwasawa decomposition.