Lagrangian submanifolds in complex space forms satisfying equality in the optimal inequality involving delta(2,...,2)
| Autor: | Xianfeng Wang, Bang-Yen Chen, Luc Vrancken |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Mean curvature Science & Technology SURFACES Holomorphic function Multiplicity (mathematics) Algebraic geometry Submanifold H-umbilical Lagrangian submanifold Combinatorics delta-invariants Complex space Lagrangian submanifold Optimal inequality Ideal submanifolds Physical Sciences Geometry and Topology Sectional curvature Invariant (mathematics) IMMERSIONS Mathematics |
| Popis: | It was proved in Chen and Dillen (J Math Anal Appl 379(1), 229–239, 2011) and Chen et al. (Differ Geom Appl 31(6), 808–819, 2013) that every Lagrangian submanifold M of a complex space form $$\tilde{M}^{n}(4c)$$ with constant holomorphic sectional curvature 4c satisfies the following optimal inequality: A $$\begin{aligned} \delta (2,\ldots ,2)\le \frac{n^2(2n-k-2)}{2(2n-k+4)} H^{2} +\frac{n^2-n-2k}{2}c, \end{aligned}$$ where $$H^{2}$$ is the squared mean curvature and $$\delta (2,\dots ,2)$$ is a $$\delta $$ -invariant on M introduced by the first author, and k is the multiplicity of 2 in $$\delta (2,\dots ,2)$$ , where $$n\ge 2k +1$$ . This optimal inequality improves an earlier inequality obtained by the first author in Chen (Jpn J Math 26(1), 105–127, 2000). The main purpose of this paper is to study Lagrangian submanifolds of $$\tilde{M}^{n}(4c)$$ satisfying the equality case of the optimal inequality (A). |
| Databáze: | OpenAIRE |
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