08/02/10 17:57:58
>>436
既に解決済みのようです
Hsiung, Chuan-Chih(1-LEHI)
Nonexistence of a complex structure on the six-sphere.
Bull. Inst. Math. Acad. Sinica 14 (1986), no. 3, 231--247.
Summary: "The purpose of this paper is to solve the long-standing unsolved problem:
Does there exist a complex structure on the $6$-sphere?"
The main theorem is too lengthy to state here, but it has the following corollaries.
Corollary 1: A Riemann $2n$-manifold $M^{2n}$ $(n\geq 2)$ of constant nonzero sectional
curvature admits a complex structure if and only if $M^{2n}$ admits a flat metric.
Corollary 2: There does not exist a complex structure on a Riemannian $2n$-manifold $M^{2n}$
$(n\geq 2)$ satisfying the following conditions:
(a) $M^{2n}$ does not admit a flat metric;
(b) $M^{2n}$ is of constant nonzero sectional curvature.
Corollary 3: There does not exist a complex structure on $S^{2n}$ for $n\geq 2$.