# Lagrangian submanifolds in complex space forms satisfying equality in the optimal inequality involving δ(2 , … , 2)

Abstract : 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 M~ n(4 c) with constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2,…,2)≤n2(2n-k-2)2(2n-k+4)H2+n2-n-2k2c,where H2 is the squared mean curvature and δ(2 , ⋯ , 2) is a δ-invariant on M introduced by the first author, and k is the multiplicity of 2 in δ(2 , ⋯ , 2) , where n≥ 2 k+ 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 M~ n(4 c) satisfying the equality case of the optimal inequality (A)
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Submitted on : Wednesday, July 13, 2022 - 2:26:19 PM
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### Citation

Bang-Yen Chen, Luc Vrancken, Xianfeng Wang. Lagrangian submanifolds in complex space forms satisfying equality in the optimal inequality involving δ(2 , … , 2). Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Springer Verlag, 2021, 62 (1), pp.251-264. ⟨10.1007/s13366-020-00541-4⟩. ⟨hal-03722520⟩

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