The six dimensional sphere is a complex manifold

Details The six dimensional sphere is a complex manifold The six dimensional sphere is a complex manifold

2005-05-30

arxiv.org/abs/math/0505634v5

Mathematics

Differential Geometry

20 pages, LaTeX, no figures; an improved and simplified version based on comments. Changes: the end of the proof of Lemma 4.1

Scientific paper

Existence of a complex structure on the six dimensional sphere is proved in this paper. The proof is based on re-interpreting a hypothetical complex structure as a classical ground state of a non-linear scalar field theory formulated on S^6. This classical vacuum solution is then constructed via Fourier expansion from the obvious one of a similar theory on the exceptional compact Lie group G_2.

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