在有紧结构的纤维捆上,奇格尔变形的概念组合在一起
Leonardo F Cavenaghi1, Lino Grama1, Llohann D Sperança2
1Instituto de Matemática, Estatística e Computação Cinetífica - Unicamp, Rua Sérgio Buarque de Holanda, 651, Campinas, SP 13083-859 Brazil.
概括
本文介绍了纤维束上的奇格变形,统一和扩展现有定理. 它展示了该技术的技术.
科学领域:
- 不同几何学微分几何学
- 拓学的拓学
- 几何分析 几何分析
背景情况:
- 奇格变形是几何分析中的一个强大的技术.
- 现有的文献缺乏对纤维捆上的奇格变形的统一方法.
研究的目的:
- 系统地在带有紧结构组的纤维束上引入奇格变形.
- 为了统一和简化几种已知的结果的恢复.
- 扩展现有关于奇格变形规范性质的研究.
主要方法:
- 在纤维捆上系统地引入奇格变形.
- 已确定的定理的统一再证明 (Schwachhöfer-Tuschmann,Fukaya,Yamaguchi).这是一个非常简单的方法.
- 延伸Searle-Solórzano-Wilhelm在规范化方面的工作.
主要成果:
- 一个统一的框架用于纤维捆上的奇格尔变形.
- 在几何分析中的关键定理的简化证明.
- 通过奇格变形来扩大对正规化性质的理解.
结论:
- 奇格变形提供了一个强大的和统一的技术.
- 这项工作标准化并促进了奇格变形的使用.
- 虽然预期,但所呈现的结果有助于该技术的广泛采用.
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