Yang-Mills, Complex Structures and Chern's Last Theorem

Details Yang-Mills, Complex Structures and Chern's Last Theorem Yang-Mills, Complex Structures and Chern's Last Theorem

2005-01-07

arxiv.org/abs/hep-th/0501050v3

Mod.Phys.Lett. A20 (2005) 2583-2600

Physics

High Energy Physics

High Energy Physics - Theory

Chern's proof remains incomplete, and we have edited some statements in our article accordingly

Scientific paper

10.1142/S0217732305018761

Recently Shiing-Shen Chern suggested that the six dimensional sphere $\mathbb{S}^6$ has no complex structure. Here we explore the relations between his arguments and Yang-Mills theories. In particular, we propose that Chern's approach is widely applicable to investigate connections between the geometry of manifolds and the structure of gauge theories. We also discuss several examples of manifolds, both with and without a complex structure.

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