# Recent developments on Oka manifolds

@article{Forstneri2020RecentDO,
title={Recent developments on Oka manifolds},
author={Franc Forstneri{\vc}},
journal={Indagationes Mathematicae},
year={2020}
}
• F. Forstnerič
• Published 14 June 2020
• Mathematics
• Indagationes Mathematicae

## References

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Oka theory has its roots in the classical Oka principle in complex analysis. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in
We investigate the behaviour of the Oka property with respect to deformations of compact complex manifolds. We show that in a family of compact complex manifolds, the set of Oka fibres corresponds to
• Yuta Kusakabe
• Mathematics
Indiana University Mathematics Journal
• 2021
We prove that Gromov's ellipticity condition $\mathrm{Ell}_1$ characterizes Oka manifolds. This characterization gives another proof of the fact that subellipticity implies the Oka property, and
Let X be a connected Oka manifold, and let S be a Stein manifold with dimS ≥ dimX. We show that every continuous map S → X is homotopic to a surjective strongly dominating holomorphic map S → X. We
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert's classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns
We study the class of compact complex manifolds whose first Chern class vanishes in the Bott-Chern cohomology. This class includes all manifolds with torsion canonical bundle, but it is strictly
• Mathematics
• 2018
In this paper we survey the theory of holomorphic approximation, from the classical nineteenth century results of Runge and Weierstrass, continuing with the twentieth century work of Oka and Weil,
. We show that the fundamental group of any smooth subelliptic variety is ﬁnite. Moreover, it is also proved that every ﬁnite group can be realized as the fundamental group of a smooth subelliptic
• Mathematics
• 2014
We give a detailed proof of Siu’s theorem on extendibility of holomorphic vector bundles of rank larger than one, and prove a corresponding extension theorem for holomorphic sprays. We apply this