郑州大学胡泽军教授学术报告 3月11日上午
发布时间: 2019-03-07 访问次数: 13

报告题目:The 3-sphere submanifolds in and in the nearly Kähler and


时间:2019-03-11 (星期一) 09:00 ~ 2019-03-11 (星期一) 10:00

 

地点:理工北楼601报告厅

 

主办:数学与信息学院, 福建省分析数学及应用重点实验室, 数学研究中心

 

参加对象:感兴趣的老师和研究生


报告摘要:In this talk, I will introduce some of our recent researches on submanifolds of the 3-sphere immersions into the complex projective space and into the homogeneous nearly Kähler manifold  and .

For the former case, we notice that the equivariant CR minimal immersions from the round 3-sphere into the complex projective space have been classified by Zhenqi Li explicitly (J London Math Soc 68 (2003), 223-240). Then, by employing the equivariant condition which implies that the induced metric is left-invariant, and that all geometric properties of endowed with a left-invariant metric can be expressed in terms of the structure constants of the Lie algebra su(2), we establish an extended classification theorem for equivariant CR minimal immersions from the 3-sphere  into  without the assumption of constant sectional curvatures.

For the latter case, we first show that isotropic Lagrangian submanifolds in any 6-dimensional strict nearly Kähler manifold are totally geodesic. Then, a complete classification of the J-isotropic Lagrangian submanifolds in the homogeneous nearly Kähler  is obtained, which mainly consists of 3-sphere immersions. Here, a Lagrangian submanifold of  is called J-isotropic if there exists a function  such that the metric , the almost complex structure J and the second fundamental form  satisfy  for all unit tangent vector .Finally, we characterize some 3-sphere immersions into the nearly Kähler  by establishing rigidity theorems.

References

[1] Zejun Hu and Yinshan Zhang, On isotropic Lagrangian submanifolds in the homogeneous nearly Kähler , Sci. China Math., 60 (2017), 671-684.

[2] Zejun Hu, Jiabin Yin and Zhenqi Li, Equivariant CR minimal immersions frominto  , Ann. Global Anal. Geom., 54 (2018), 1-24.

[3] Zejun Hu and Jiabin Yin, Equivariant minimal immersions from  into  , Acta Math. Scientia, 39B(4) (2019), 151-166.

[4] Zejun Hu, Jiabin Yin and Bangchao Yin, Rigidity theorems of Lagrangian submanifolds in the homogeneous nearly Kähler, arXiv: 1902.01641v2.

 

报告人简介:胡泽军教授,男,1996年获四川大学基础数学理学博士学位(导师李安民院士),研究方向为微分几何,现任郑州大学数学与统计学院教授、博士生导师,河南省数学会理事。20021月至20031月在国家出国留学基金资助下赴德国柏林工业大学学习访问。JDG等顶级微分几何等杂志上发表了30多篇SCI论文。