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

2017/05/01 by Chen, Bang-Yen, Dillen, Franki, Van der Veken, Joeri +1
#53C40 #53D12 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.00685

Abstract

It was proven in [B.-Y. Chen, F. Dillen, J. Van der Veken and L. Vrancken, Curvature inequalities for Lagrangian submanifolds: the final solution, Differ. Geom. Appl. 31 (2013), 808-819] that every Lagrangian submanifold M of a complex space form Mⁿ(4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: δ(2,n-2) ≤ (n²(n-2))/(4(n-1)) 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 Mⁿ(4c), n ≥ 5, which satisfy the equality case of this inequality at every point.

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