In April 2003, Chern began a study of almost-complex structures on the six-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group G2. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on S6, he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on S6.

中文翻译：

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S.-S。陈对六球体上几乎复杂结构的研究

2003 年 4 月，陈先生开始研究六球上的准复结构，其想法是利用其著名的异群下准复结构不变量的特殊性质G2. 虽然他没有解决（目前仍然悬而未决的）确定是否存在可积的几乎复杂结构的问题小号6，他确实证明了一个重要的身份，它解决了一类有趣的几乎复杂结构的问题小号6.