188比分直播

Results related with complex structures on S^6

发布者:文明办发布时间:2024-04-26浏览次数:81

主讲人:彦文娇 北京师范大学教授


时间:2024年4月26日9:00


地点:腾讯会议 261 518 487


举办单位:数理学院


主讲人介绍:彦文娇,北京师范大学数学科学学院教授,博导。主要研究微分几何,特别是等参理论的研究与应用。代表性成果包括完全解决了等参情形的丘成桐第一特征值猜想,给出Besse在经典专著《爱因斯坦流形》中挑战性问题的系列单连通例子,给出陈省身猜想的任意维数的最新进展等。多篇论文发表在国际著名学术期刊 JDG, Adv. Math., JFA, IMRN等。2


内容介绍: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.