Linked from

The 27 pages that link to Isometry, each with the reason it gives.

• Metric spaceRelated: It identifies structure-preserving transformations of metric spaces.

• Euclidean spaceRelated: Isometries preserve Euclidean structure even when coordinates or positions change.

• Euclidean distanceRelated: Euclidean isometries preserve this distance under translations, rotations, and reflections.

• Affine transformationCompared with: An affine map may stretch or shear, while an isometry cannot change distances.

• Hyperbolic geometryRelated: Hyperbolic isometries preserve the geometry while moving points and geodesics.

• AllometryCompared with: It provides the null case against which allometric change is measured.

• Congruence (geometry)Related: Isometries formalize the transformations that carry one congruent figure onto another.

• HomeomorphismCompared with: An isometry preserves metric measurements that a homeomorphism may freely distort.

• Point groupRelated: The geometric symmetries in ordinary point groups preserve distances.

• Affine geometryCompared with: Isometries preserve distances, a constraint absent from affine geometry.

• Conformal mapCompared with: Isometries preserve lengths as well as angles, a stronger condition than conformality.

• Space groupNarrower topic: Space-group operations are isometries constrained to preserve a periodic arrangement.

• Similarity (geometry)Compared with: An isometry preserves size, whereas similarity permits uniform scaling.

• Euclidean planeRelated: Isometries capture the plane’s rigid motions without changing its geometry.

• Similarity transformationCompared with: Isometries preserve every length, whereas similarities may multiply all lengths by one factor.

• Rigid motionRelated: Rigid motion is the Euclidean-space case of this broader concept.

• Theorema EgregiumRelated: The theorem concerns what curvature survives when a surface is bent without stretching.

• Rotation groupNarrower topic: Rotations are isometries, so preservation of distance constrains the group.

• Gromov–Hausdorff convergenceRelated: The convergence notion treats isometric spaces as identical, regardless of their point labels or presentation.

• Kirszbraun theoremRelated: Hilbert-space embeddings help relate the Euclidean theorem to broader metric settings.

• Inversive geometryCompared with: Inversion is not an isometry because distances vary with position relative to its center.

• Mazur–Ulam theoremCompared with: Without surjectivity, isometries need not be affine, so the theorem’s hypothesis is essential.

• Mostow rigidity theoremRelated: The theorem upgrades topological equivalence to an isometry of hyperbolic manifolds.

• Banach–Mazur theoremRelated: The theorem asserts a linear embedding that preserves the Banach-space norm exactly.

• Cartan–Dieudonné theoremNarrower topic: The theorem concerns linear isometries of quadratic spaces.

• Doris SchattschneiderRelated: Isometries describe how repeated figures move across a tessellated plane.

• Dvoretzky's theoremRelated: Exact isometric copies of Euclidean spaces are stronger than the theorem's approximate copies.