Results related with complex structures on S^6

發(fā)布者:文明辦發(fā)布時(shí)間:2024-04-26瀏覽次數(shù):81

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《愛因斯坦流形》中挑戰(zhàn)性問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.