Results related with complex structures on S^6

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.