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In differential geometry, the term homogeneous space refers to the quotient space of a Lie group modulo a closed subgroup, which results in a manifold with a smooth transitive action of the Lie group. Instead, in metric geometry and, more generally, in analysis on metric spaces, the term homogeneous often refers to functions that, when precomposed with dilations of the space, scale by certain constants; see Exercise 6.6.12.

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Metric Groups and Homogeneous Spaces

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  • 发表日期：

    2025年

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  • Enrico Le Donne

摘要

In differential geometry, the term homogeneous space refers to the quotient space of a Lie group modulo a closed subgroup, which results in a manifold with a smooth transitive action of the Lie group. Instead, in metric geometry and, more generally, in analysis on metric spaces, the term homogeneous often refers to functions that, when precomposed with dilations of the space, scale by certain constants; see Exercise 6.6.12.