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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:458

Article

Chen, Bang-Yen¹  Dillen, Franki²  Van der Veken, Joeri²  Vrancken, Luc^2,3 

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

[2] Katholieke Univ Leuven, Dept Math, Celestijnenlaan 200 B,Box 2400, BE-3001 Leuven, Belgium

[3] Univ Valenciennes, LAMAV, ISTV2, Campus Mt Houy, F-59313 Valenciennes 9, France

关键词: Lagrangian submanifold;    optimal inequality;    delta-invariant;    ideal submanifold;   

DOI  :  10.1016/j.jmaa.2017.10.044

来源: Elsevier

【 摘 要 】

It was proven in [4] that every Lagrangian submanifold M of a complex space form (M) over tilde (n)(4c) of constant holomorphic sectional curvature 4c satisfies the following optimal inequality: delta(2, n - 2) <= n(2)(n - 2)/4(n - 1) H-2 + 2(n - 2)c, where H-2 is the squared mean curvature and delta(2, n - 2) is a S-invariant on M. In this paper we classify Lagrangian submanifolds of complex space forms (M) over tilde (n)(4c), n >= 5, which satisfy the equality case of this improved inequality at every point. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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