Transitivity domains of groups of similarities (Q1114163)
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scientific article; zbMATH DE number 4084456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Transitivity domains of groups of similarities |
scientific article; zbMATH DE number 4084456 |
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Transitivity domains of groups of similarities (English)
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1988
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In this nicely written paper, the author shows by means of elementary and well-known results from Euclidean geometry that if a group G of similarities acts transitively on an open subset X of a real affine n- space then, essentially, X is \(A^ n\) or a half-space or a complement of a lower dimensional affine subspace. He also points out applications of his result to Riemannian structures and to convex geometry.
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transitive action
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Euclidean geometry
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similarities
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affine n-space
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