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Some Remarks on the Group of Isometries of a Metric Space

In: Nonlinear Analysis

Author

Listed:
  • Dorin Andrica

    (“Babeş-Bolyai” University
    King Saud University)

  • Vasile Bulgarean

    (“Babeş-Bolyai” University)

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.

Suggested Citation

  • Dorin Andrica & Vasile Bulgarean, 2012. "Some Remarks on the Group of Isometries of a Metric Space," Springer Optimization and Its Applications, in: Panos M. Pardalos & Pando G. Georgiev & Hari M. Srivastava (ed.), Nonlinear Analysis, edition 127, chapter 0, pages 57-64, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-3498-6_4
    DOI: 10.1007/978-1-4614-3498-6_4
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    Cited by:

    1. Sheng Bau & Yiming Lei, 2022. "The Groups of Isometries of Metric Spaces over Vector Groups," Mathematics, MDPI, vol. 10(23), pages 1-9, November.

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