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Lagrangian submanifolds in complex space forms satisfying an improved equality involving δ(2,2)

 

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Author: Chen, Bang-Yen
Prieto Martín, Alicia
Wang, Xianfeng
Department: Universidad de Sevilla. Departamento de Geometría y Topología
Date: 2013
Published in: Publicationes Mathematicae, 82 (1), 193-217.
Document type: Article
Abstract: It was proved in [8, 9] that every Lagrangian submanifold M of a complex space form M˜ 5 (4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2, 2) ≤ 25 4 H 2 + 8c, (A) where H 2 is the squared mean curvature and δ(2, 2) is a δ-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 M˜ 5 (4c) satisfying the equality case of the improved inequality (A).
Cite: Chen, B., Prieto Martín, A. y Wang, X. (2013). Lagrangian submanifolds in complex space forms satisfying an improved equality involving δ(2,2). Publicationes Mathematicae, 82 (1), 193-217.
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URI: http://hdl.handle.net/11441/42617

DOI: http://dx.doi.org/10.5486/PMD.2013.5405

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