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Journal Articles Journal of Mathematical Analysis and Applications Year : 2018

Classification of δ(2,n − 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms

Abstract

It was proven in [4] that every Lagrangian submanifold M of a complex space form M˜n(4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2,n−2)≤[Formula presented]H2+2(n−2)c, where H2 is the squared mean curvature and δ(2,n−2) is a δ-invariant on M. In this paper we classify Lagrangian submanifolds of complex space forms M˜n(4c), n≥5, which satisfy the equality case of this improved inequality at every point.

Dates and versions

hal-03233923 , version 1 (25-05-2021)

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Bang-Yen Chen, Franki Dillen, Joeri van Der Veken, Luc Vrancken. Classification of δ(2,n − 2)-ideal Lagrangian submanifolds in n-dimensional complex space forms. Journal of Mathematical Analysis and Applications, 2018, 458 (2), pp.1456-1485. ⟨10.1016/j.jmaa.2017.10.044⟩. ⟨hal-03233923⟩
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