English

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

High Energy Physics - Theory 2009-11-11 v3

Abstract

Recently Shiing-Shen Chern suggested that the six dimensional sphere S6\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.

Cite

@article{arxiv.hep-th/0501050,
  title  = {Yang-Mills, Complex Structures and Chern's Last Theorem},
  author = {Andrei Marshakov and Antti J. Niemi},
  journal= {arXiv preprint arXiv:hep-th/0501050},
  year   = {2009}
}

Comments

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