Gray, Alfred A property of a hypothetical complex structure on the six sphere. (English) Zbl 0891.53018 Boll. Unione Mat. Ital., VII. Ser., B 11, No. 2, Suppl., 251-255 (1997). A long standing problem in differential geometry is the existence of a complex structure on the six-dimensional sphere \(S^6\). Several proofs have been given, but none has been accepted by the mathematical community. In this paper, the author supposes that there exists a complex structure on the six-sphere. For such a hypothetical complex structure, Dolbeault cohomology groups \(H^{p,q} (S^6)\) would be defined. It is proved that then \(\dim H^{0,1} (S^6)\geq 1\). Reviewer: M.Fernandez (Bilbao) Cited in 1 ReviewCited in 3 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C55 Global differential geometry of Hermitian and Kählerian manifolds Keywords:6-sphere; complex structure; Dolbeault cohomology groups PDF BibTeX XML Cite \textit{A. Gray}, Boll. Unione Mat. Ital., VII. Ser., B 11, No. 2, 251--255 (1997; Zbl 0891.53018)