Complex parallelizable manifolds. (English) Zbl 0917.32005
Noguchi, J. (ed.) et al., Geometric complex analysis. Proceedings of the conference held at the 3rd International Research Institute of the Mathematical Society of Japan, Hayama, March 19–29, 1995. Singapore: World Scientific. 667-678 (1996).
The introduction: “We give a survey of our recent results on complex-parallelizable manifolds, most of which are contained in [J. Winkelmann, ‘Complex analytic geometry of complex parallelizable manifolds’, Habil. schrift (1994)]. For our purposes it is useful to call a complex manifold parallelizable if it is biholomorphic to a quotient of a complex Lie group \(G\) by a discrete subgroup \(\Gamma\). By a result of H.-C. Wang [Proc. Am. Math. Soc. 5, 771-776 (1954; Zbl 0056.15403)] for a compact complex manifold this condition is equivalent to the assumption that the tangent bundle is holomorphically trivial. A compact complex parallelizable manifold is Kähler if and only if \(G\) is commutative, i.e. if and only if it is a torus”.
For the entire collection see [Zbl 0903.00037].
For the entire collection see [Zbl 0903.00037].
Reviewer: G.Ehrig (Berlin)
MSC:
32C15 | Complex spaces |
32J18 | Compact complex \(n\)-folds |
22E10 | General properties and structure of complex Lie groups |