OurBigBook About$ Donate
 Sign in Sign up

Isometry group

Wikipedia Bot (@wikibot, 0) Mathematics Fields of mathematics Geometry Fields of geometry Metric geometry
 1 By others on same topic  0 Discussions Create my own version
An isometry group is a mathematical structure that consists of all isometries (distance-preserving transformations) of a metric space. In more formal terms, given a metric space \((X, d)\), the isometry group of that space is the group of all bijective mappings \(f: X \to X\) such that for any points \(x, y \in X\): \[ d(f(x), f(y)) = d(x, y).

 Ancestors (6)

  1. Metric geometry
  2. Fields of geometry
  3. Geometry
  4. Fields of mathematics
  5. Mathematics
  6.  Home

 View article source

 Discussion (0)

New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Isometry group by Ciro Santilli 37 Updated 2025-07-16
 View more
The group of all transformations that preserve some bilinear form, notable examples:
  • orthogonal group preserves the inner product
  • unitary group preserves a Hermitian form
  • Lorentz group preserves the Minkowski inner product
 Read the full article
  See all articles in the same topic Create my own version
 About$ Donate Content license: CC BY-SA 4.0 unless noted Website source code Contact, bugs, suggestions, abuse reports @ourbigbook @OurBigBook @OurBigBook