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Lagrangian submanifolds in complex space forms satisfying an improved equality involving $delta(2,2)$ | | Bang-Yen Chen
; Alicia Prieto-Marín
; Xianfeng Wang
; | | Date: |
15 Jul 2013 | | Abstract: | It was proved in [8,9] that every Lagrangian submanifold $M$ of a complex
space form $ ilde M^{5}(4c)$ of constant holomorphic sectional curvature $4c$
satisfies the following optimal inequality: {align} ag{A}delta(2,2)leq
ext{small${25}{4}$} H^{2}+8c,{align} where $H^{2}$ is the squared mean
curvature and $delta(2,2)$ is a $delta$-invariant on $M$ introduced by the
first author. This optimal inequality improves a special case of an earlier
inequality obtained in [B.-Y. Chen, Japan. J. Math. 26 (2000), 105-127].
The main purpose of this paper is to classify Lagrangian submanifolds of
$ ilde M^{5}(4c)$ satisfying the equality case of the improved inequality (A). | | Source: | arXiv, 1307.3968 | | Services: | Forum | Review | PDF | Favorites | |
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