Results related with complex structures on S^6

主講人：彥文嬌 北京師范大學(xué)教授

時(shí)間：2024年4月26日9：00

地點(diǎn)：騰訊會(huì)議 261 518 487

舉辦單位：數(shù)理學(xué)院

主講人介紹:彥文嬌，北京師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授，博導(dǎo)。主要研究微分幾何，特別是等參理論的研究與應(yīng)用。代表性成果包括完全解決了等參情形的丘成桐第一特征值猜想，給出Besse在經(jīng)典專著《愛(ài)因斯坦流形》中挑戰(zhàn)性問(wèn)題的系列單連通例子，給出陳省身猜想的任意維數(shù)的最新進(jìn)展等。多篇論文發(fā)表在國(guó)際著名學(xué)術(shù)期刊 JDG, Adv. Math., JFA, IMRN等。2

內(nèi)容介紹：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.