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 from
into 
, 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。2002年1月至2003年1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。
