English

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

Differential Geometry 2021-11-30 v2

Abstract

In 2003, S.-s. Chern began a study of almost-complex structures on the 6-sphere, with the idea of exploiting the special properties of its well-known almost-complex structure invariant under the exceptional group G2G_2. While he did not solve the (currently still open) problem of determining whether there exists an integrable almost-complex structure on the 6-sphere, he did prove a significant identity that resolves the question for an interesting class of almost-complex structures on the 6-sphere.

Cite

@article{arxiv.1405.3405,
  title  = {S.-S. Chern's study of almost-complex structures on the six-sphere},
  author = {Robert L. Bryant},
  journal= {arXiv preprint arXiv:1405.3405},
  year   = {2021}
}

Comments

12 pages, no figures. Some essential references have been added in this version that I was unaware of when I wrote Version 1

R2 v1 2026-06-22T04:13:42.847Z