几何结构刚度

IF 0.5 4区数学 Q3 MATHEMATICS

Geometriae Dedicata Pub Date : 2023-11-20 DOI:10.1007/s10711-023-00861-4

Ursula Hamenstädt, Frieder Jäckel

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引用次数: 0

摘要

流形M上的几何结构是由具有齐次空间G/H中值的图对M的覆盖而产生的，具有G元素的图迁移限制。如果M是非球面的，则这种几何结构由M的基本群与G的同态给出。这种结构的刚性意味着同态的共轭类可以由M上的拓扑或几何信息重构。着重于拓扑类型和长度函数。

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Rigidity of geometric structures

Geometric structures on a manifold M arise from a covering of M by charts with values in a homogeneous space G/H, with chart transitions restrictions of elements of G. If M is aspherical, then such geometric structures are given by a homomorphism of the fundamental group of M into G. Rigidity of such structures means that the conjugacy class of the homomorphism can be reconstructed from topological or geometric information on M. We give an overview of such rigidity results, focusing on topological type and length functions.

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来源期刊

Geometriae Dedicata 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Geometriae Dedicata concentrates on geometry and its relationship to topology, group theory and the theory of dynamical systems. Geometriae Dedicata aims to be a vehicle for excellent publications in geometry and related areas. Features of the journal will include: A fast turn-around time for articles. Special issues centered on specific topics. All submitted papers should include some explanation of the context of the main results. Geometriae Dedicata was founded in 1972 on the initiative of Hans Freudenthal in Utrecht, the Netherlands, who viewed geometry as a method rather than as a field. The present Board of Editors tries to continue in this spirit. The steady growth of the journal since its foundation is witness to the validity of the founder''s vision and to the success of the Editors'' mission.