Conformally flat, minimal, Lagrangian submanifolds in complex space forms  

作　　者：Miroslava Antić Luc Vrancken 

机构地区：[1]Faculty of Mathematics,University of Belgrade,Belgrade 11000,Serbia [2]Laboratoire de Mathématiques pour l’Ingénieur,Université Polytechnique Hauts-de-France,Valenciennes 59313,France [3]Departement Wiskunde,Katholieke Universiteit Leuven,Leuven 3001,Belgium

出　　处：《Science China Mathematics》2022年第8期1641-1660,共20页中国科学：数学（英文版）

基　　金：supported by the Ministry of Education,Science and Technological Development of the Republic of Serbia(Grant No.174012)。

摘　　要：We investigate n-dimensional(n≥4),conformally flat,minimal,Lagrangian submanifolds of the n-dimensional complex space form in terms of the multiplicities of the eigenvalues of the Schouten tensor and classify those that admit at most one eigenvalue of multiplicity one.In the case where the ambient space is Cn,the quasi umbilical case was studied in Blair(2007).However,the classification there is not complete and several examples are missing.Here,we complete(and extend) the classification and we also deal with the case where the ambient complex space form has non-vanishing holomorphic sectional curvature.

关 键 词：Lagrangian submanifolds conformally flat complex space form warped product submanifold 

分 类 号：O186.1[理学—数学]