Lagrangian submanifolds in the 6-dimensional nearly Kähler manifolds with parallel second fundamental form

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• 作者：Y. Zhang^a ; ^{zhangysookk@163.com" class="auth_mail" title="E-mail the corresponding author} ; B. Dioos^b ; ^{bart.dioos@kuleuven.be" class="auth_mail" title="E-mail the corresponding author} ; Z. Hu^a ; ^{huzj@zzu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; L. Vrancken^c ; ^b ; ^{luc.vrancken@univ-valenciennes.fr" class="auth_mail" title="E-mail the corresponding author} ; X. Wang^d ; ^{wangxianfeng@nankai.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：53B25 ; 53C24 ; 53C42
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：108
• 期：Complete
• 页码：21-37
• 全文大小：482 K

文摘

In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kähler k to view the MathML source">S³×S³ with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kähler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kähler k to view the MathML source">S³×S³.