Minimal Lagrangian submanifolds of the complex hyperquadric
| Autor: | Luc Vrancken, Joeri Van der Veken, Xianfeng Wang, Hui Ma, Haizhong Li |
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| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Gauss map Mathematics::Complex Variables General Mathematics 010102 general mathematics Submanifold 01 natural sciences symbols.namesake Hypersurface Principal curvature 0103 physical sciences symbols Immersion (mathematics) Mathematics::Differential Geometry 010307 mathematical physics 0101 mathematics Special case Mathematics::Symplectic Geometry Lagrangian Structural approach Mathematics |
| Zdroj: | Science China Mathematics. 63:1441-1462 |
| ISSN: | 1869-1862 1674-7283 |
| DOI: | 10.1007/s11425-019-9551-2 |
| Popis: | We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures. In particular, we define local angle functions encoding the geometry of the Lagrangian submanifold at hand. We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface. We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvatures and all minimal Lagrangian submanifolds for which all local angle functions, respectively all but one, coincide. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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