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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 [Formula: see text]. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on [Formula: see text], he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on [Formula: see text].

S.-S. Chern’s study of almost-complex structures on the six-sphere