Classification of $\delta(2,n-2)$-ideal Lagrangian submanifolds in $n$-dimensional complex space forms
| Autor: | Joeri Van der Veken, Franki Dillen, Bang-Yen Chen, Luc Vrancken |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Mathematics - Differential Geometry
Holomorphic function 01 natural sciences Combinatorics symbols.namesake Complex space 0103 physical sciences Sectional curvature Ideal (ring theory) 0101 mathematics Mathematics::Symplectic Geometry Mathematics 53D12 53C40 Mean curvature 010308 nuclear & particles physics Applied Mathematics 010102 general mathematics ideal submanifold optimal inequality Submanifold delta-invariant Lagrangian submanifold symbols Mathematics::Differential Geometry Constant (mathematics) Analysis Lagrangian |
| Popis: | It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold $M$ of a complex space form $\tilde M^{n}(4c)$ of constant holomorphic sectional curvature $4c$ satisfies the following optimal inequality: \begin{align*} \delta(2,n-2) \leq \frac{n^2(n-2)}{4(n-1)} H^2 + 2(n-2) c, \end{align*} where $H^2$ is the squared mean curvature and $\delta(2,n-2)$ is a $\delta$-invariant on $M$. In this paper we classify Lagrangian submanifolds of complex space forms $\tilde M^{n}(4c)$, $n \geq 5$, which satisfy the equality case of this inequality at every point. Comment: 26 pages |
| Databáze: | OpenAIRE |
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