Hartogs phenomenon and the problem of complex spheres
Zouaoui Mekri
TL;DR
This paper investigates whether the six-dimensional sphere S^6 can admit a complex structure, concluding negatively and addressing a long-standing question in differential geometry.
Contribution
The paper provides a negative answer to the existence of complex structures on S^6, clarifying a fundamental geometric problem.
Findings
No complex structure exists on S^6
Addresses the Hartogs phenomenon in relation to complex spheres
Contributes to understanding of complex structures on real manifolds
Abstract
In this paper, we solve in the negative the following problem : Is there any complex structure on the sphere S^6?
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Mathematics and Applications