The complex structure on the six dimensional sphere
Gabor Etesi

TL;DR
This paper proves the existence of a complex structure on the six-dimensional sphere and explicitly computes its integrable almost complex tensor using octonion automorphisms, revealing a complex and perplexing tensor field.
Contribution
It provides a new proof of the complex structure on the six-sphere and explicitly computes its tensor using octonion automorphisms, which is a novel and detailed approach.
Findings
Existence of a complex structure on the six-sphere confirmed.
Explicit computation of the integrable almost complex tensor achieved.
The resulting tensor field is complex and intricate.
Abstract
Proof of existence of a complex structure on the six-sphere, followed by an explicit computation of its underlying integrable almost complex tensor by the aid of inner automorphisms of the octonions, is exhibited. Both are elementary and self-contained however the size and complexity of the emerging almost complex tensor field on the six-sphere is perplexing.
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Taxonomy
TopicsAdvanced Differential Geometry Research · Nonlinear Waves and Solitons · Geometric Analysis and Curvature Flows
