Article
Lagrangian submanifolds in complex space forms satisfying an improved equality involving δ(2,2)
Author/s | Chen, Bang-Yen
Prieto Martín, Alicia Wang, Xianfeng |
Department | Universidad de Sevilla. Departamento de Geometría y Topología |
Publication Date | 2013 |
Deposit Date | 2016-06-22 |
Published in |
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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 ... 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). |
Funding agencies | Universidad de Sevilla National Natural Science Foundation of China |
Project ID. | 11171175 |
Citation | 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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