北航数学论坛学术报告

微分几何讨论班（2024春第7讲）

Results related with complex structures on S^6

彦文娇 教授

(北京师范大学)

时间：2024年5月29日（周三上午）14：30-15：30

地点：沙河主E404

摘要: It is a longstanding problem that whether there exists a complex structure on the 6-dimensional sphere? Many famous mathematicians have made efforts on this problem, such as Hopf, Wen-tsun Wu, Borel, Serre, LeBrun, Shiing-Shen Chern, Atiyah, etc. This talk consists of two parts. (i) Taking advantage of isoparametric theory, we construct complex structures on certain isoparametric hypersurfaces in the unit sphere. As a consequence, there is a closed 8-dimensional manifold N^8 such that there exists a complex structure on S^6×N^8. (ii) As a generalization of LeBrun's result, we prove that there is no orthogonal almost complex structure on the standard S^6 with the length of Nijenhuis tensor is smaller than a certain constant everywhere. This talk is based on joint works with Professor Zizhou Tang..

报告人简介: 彦文娇，北京师范大学数学学院教授，博士生导师，入选国家级青年人才项目。主要研究方向为微分几何，特别是等参超曲面等参函数及其相关应用的研究，至今已在JDG, Adv. Math., JFA, IMRN, Sci. China Math.等国际著名数学期刊上发表多篇论文。代表性成果有与唐梓洲教授合作完全解决了等参情形的丘成桐第一特征值猜想、给出陈省身猜想在任意维数的部分进展等。

邀请人：谢振肖

欢迎大家参加！