Some Remarks on the Group of Isometries of a Metric Space

Dorin Andrica () and Vasile Bulgarean ()
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Dorin Andrica: “Babeş-Bolyai” University
Vasile Bulgarean: “Babeş-Bolyai” University

Chapter Chapter 4 in Nonlinear Analysis, 2012, pp 57-64 from Springer

Abstract: Abstract The main purpose of this paper is to describe the isometry groups $\mathit{Iso}_{d_{p}}(\mathbb{R}^{n})$ for p≥1, p≠2, and p=∞, where the metric d p is given by (4.2). A corollary of the main result contained in Theorem 4.1 and Theorem 4.2 is that in case p≠2 all these groups are isomorphic and, consequently, they are independent of p. In the last section, the isometry dimension of a finite group with respect to a given metric on the space ℝ n is introduced.

Keywords: Isometry with respect to a metric; Group of isometries; Translations group of the Euclidean n-space; Taxicab metric; Mazur–Ulam theorem; Semi-direct product of groups; 51B20; 51F99; 51K05; 51K99; 51N25 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3498-6_4

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