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04 July 2020
  » arxiv » 1307.3968

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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
AbstractIt 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
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