A Note On the Nonexistence of a Complex Threefold as a Conjugate Orbit of G2
A Note On the Nonexistence of a Complex Threefold as a Conjugate Orbit of G2
复制标题
关于G2共轭轨道复三重不存在的注解
DOI：
10.1007/s00025-022-01678-5
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发表时间：
2022
影响因子：
2.2
通讯作者：
Zhonghua Wang
中科院分区：
文献类型：
--
作者：
Daniel Guan;Zhonghua Wang
S6上存在或不存在复杂结构是一个长期未解决的问题。在G2中有一个著名的轨道O（Λ），它与S6同构，并且被G'abor Etesi用来寻找一个复杂的结构。Etesi建议通过这个轨道在S6中给出一个复杂的结构。在丹尼尔关的早期论文中，他证明了轨道不可能是复子流形。由于该文献中对O（Λ）到S6的映射没有明确的描述，本文给出了该结果的另一个更清楚、更简单、更明确的证明.
The existence or nonexistence of a complex structure on S6 was a long standing unsolved problem. There is a well-known orbit O(Λ) in G2 which is diffeomorphic to S6 and used by G´abor Etesi in an effort to find a complex structure. Etesi suggested to give a complex structure in S6 through this orbit. In Daniel Guan’s earlier paper, he proved that the orbit can not be a complex submanifold. Since there was not a clear description of the map from O(Λ) to S6 in that paper, we give another clearer, simpler and explicit proof of that result in this paper.