全纯Cartan几何的变形理论，II

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2022-01-01 DOI:10.1515/coma-2021-0129

I. Biswas, Sorin Dumitrescu, G. Schumacher

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引用次数: 0

摘要

在[4]的延续中，我们研究了允许底层复流形移动的全纯Cartan几何的变形。计算了平面全纯卡尔坦几何的无穷小变形空间。我们证明了从平坦全纯卡尔坦几何的无穷小变形到拓扑流形上底层平坦主束的无穷小变形的自然遗忘映射是同构的。

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Deformation theory of holomorphic Cartan geometries, II

Abstract In this continuation of [4], we investigate the deformations of holomorphic Cartan geometries where the underlying complex manifold is allowed to move. The space of infinitesimal deformations of a flat holomorphic Cartan geometry is computed. We show that the natural forgetful map, from the infinitesimal deformations of a flat holomorphic Cartan geometry to the infinitesimal deformations of the underlying flat principal bundle on the topological manifold, is an isomorphism.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.