37000gcom威尼斯2024第 8 期 数理大讲堂

主讲人： 彦文娇 教授（北京师范大学）

主持人： 唐梓洲 教授（南开大学）

讲座时间：2024年4月10日上午9:30-10:20

讲座地点：37000gcom威尼斯岩松堂白鹿厅

讲座题目：Results related with complex structures on S^6

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.