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Parallelizable manifolds without complex structure

Shing-Tung Yau

Complex Variables and Complex Analysis mathscidoc:1912.43583

Topology, 15, (1), 51-53, 1976.1
THEOREM 1. Let M be a compact two dimensional complex manifold with zero Euler number. Suppose there is a basis {a,, aZ, a3, a3 of the first real cohomology group H(M, R) such that the cup product a, U u2 U (Ye U LY~ is not zero. Then either M is biholomorphic to the complex torus or M is covered by the euclidean space.
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@inproceedings{shing-tung1976parallelizable,
  title={Parallelizable manifolds without complex structure},
  author={Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204225730938147},
  booktitle={Topology},
  volume={15},
  number={1},
  pages={51-53},
  year={1976},
}
Shing-Tung Yau. Parallelizable manifolds without complex structure. 1976. Vol. 15. In Topology. pp.51-53. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204225730938147.
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