Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2018-08-24 DOI:10.1515/coma-2019-0012

Hiroki Yagisita

引用次数: 7

Abstract

Abstract Let Γ(M) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X. In this paper, we introduce a C(X)-manifold structure on Γ(M). Especially, if X is contractible, then Γ(M) is a finite-dimensional C(X)-manifold. Here, C(X) denotes the Banach algebra of all complex-valued continuous functions on X.

查看原文本刊更多论文

交换巴拿赫代数上的有限维复流形与紧复流形的连续族

摘要设Γ(M)为紧致Hausdorff空间X上紧致复流形连续族M的所有全局连续截面的集合。本文在Γ(M)上引入了一个C(X)-流形结构。特别地，如果X是可压缩的，则Γ(M)是一个有限维C(X)流形。这里，C(X)表示X上所有复值连续函数的Banach代数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.