Displaying similar documents to “Fibrations of compact Kähler manifolds in terms of cohomological properties of their fundamental groups”

On holomorphic maps into compact non-Kähler manifolds

Masahide Kato, Noboru Okada (2004)

Annales de l’institut Fourier

Similarity:

We study the extension problem of holomorphic maps σ : H → X of a Hartogs domain H with values in a complex manifold X . For compact Kähler manifolds as well as various non-Kähler manifolds, the maximal domain Ω σ of extension for σ over Δ is contained in a subdomain of Δ . For such manifolds, we define, in this paper, an invariant Hex n ( X ) using the Hausdorff dimensions of the singular sets of σ ’s and study its properties to deduce informations on the complex structure of X .

Two remarks on Kähler homogeneous manifolds

Bruce Gilligan, Karl Oeljeklaus (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

We prove that every Kähler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algebraic groups in the case where the isotropy has the property that its intersection with the radical is Zariski dense in the radical.

Holomorphic Cartan geometries and rational curves

Indranil Biswas, Benjamin McKay (2016)

Complex Manifolds

Similarity:

We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.