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

JOURNAL OF GEOMETRY AND PHYSICS

卷:108

Article

Zhang, Y.¹  Dioos, B.²  Hu, Z.¹  Vrancken, L.^2,3  Wang, X.^4,5 

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

[2] Katholieke Univ Leuven, Dept Wiskunde, Celestijnenlaan 200B, B-3001 Leuven, Belgium

[3] Univ Valenciennes, LAMAV, Campus Mt Houy, F-593139 Valenciennes 9, France

[4] Nankai Univ, Sch Math Sci, Tianjin 300071, Peoples R China

[5] Nankai Univ, LPMC, Tianjin 300071, Peoples R China

关键词: Nearly Miller S-3 x S-3;    Lagrangian submanifolds;    Totally geodesic;    Parallel second fundamental form;    Berger sphere;   

DOI  :  10.1016/j.geomphys.2016.06.004

来源: Elsevier

【 摘 要 】

In this paper, we study the Lagrangian submanifolds in the homogeneous nearly Kahler S-3 x S-3 with parallel second fundamental form. We first prove that every Lagrangian submanifold with parallel second fundamental form in any 6-dimensional strict nearly Kahler manifold is totally geodesic. Then we give a complete classification of the totally geodesic Lagrangian submanifolds in the homogeneous nearly Kahler S-3 x S-3. (C) 2016 Elsevier B.V. All rights reserved.

【 授权许可】

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