g型结构的无扭连接

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-11-19 DOI:10.1016/j.difgeo.2023.102075

Brice Flamencourt

引用次数: 0

摘要

证明了对于李群SOn(R)∧G∧GLn(R)，光滑流形上的任何G结构都可以被赋予一个无扭转连接，该连接局部是给定共形类中黎曼度规的Levi-Civita连接。在这个过程中，我们对可接受的群体进行分类。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Torsion-free connections on G-structures

We prove that for a Lie group ${SO}_{n} (R) \subset G \subset {GL}_{n} (R)$ , any G-structure on a smooth manifold can be endowed with a torsion free connection which is locally the Levi-Civita connection of a Riemannian metric in a given conformal class. In this process, we classify the admissible groups.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.