Recent developments on Oka manifolds

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



Survey of Oka theory

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

Deformations of Oka manifolds

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

Elliptic characterization and localization of Oka manifolds

  • 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

Surjective Holomorphic Maps onto Oka Manifolds

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 manifolds: From Oka to Stein and back

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

Oka maps

Non-Kähler Calabi-Yau manifolds

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

Holomorphic Approximation: The Legacy of Weierstrass, Runge, Oka–Weil, and Mergelyan

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,

On the fundamental groups of subelliptic varieties

. 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

The Hartogs extension theorem for holomorphic vector bundles and sprays

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