The Hartogs extension phenomenon for holomorphic parabolic and reductive geometries

Abstract

Every holomorphic effective parabolic or reductive geometry on a domain over a Stein manifold extends uniquely to the envelope of holomorphy of the domain. This result completes the open problems of my earlier paper on extension of holomorphic geometric structures on complex manifolds. We use this result to classify the Hopf manifolds which admit holomorphic reductive geometries, and to classify the Hopf manifolds which admit holomorphic parabolic geometries. Every Hopf manifold which admits a holomorphic parabolic geometry with a given model admits a flat one. We classify flat holomorphic parabolic geometries on Hopf manifolds.

21 pages

References in corpus (5)

• Holomorphic Parabolic Geometries and Calabi-Yau Manifolds
• Complete complex parabolic geometries
• Extra extension properties of equidimensional holomorphic mappings: results and open questions
• Complex homogeneous surfaces
• Holomorphic geometric structures on Kaehler-Einstein manifolds