Isometry (2592 bytes)
1: ...[[geometry]] and [[mathematical analysis]], an '''isometry''' is a [[bijective]] distance-preserving mapping...
5: ...'arcwise isometry''. Both are often called just ''isometry'' and you should guess from context which one is ...
9: ...eserving map. A '''path isometry''' or '''arcwise isometry''' is a map which preserves the [[Curve|lengths o...
15: is a path isometry but not a global isometry.
17: ...orm a group with respect to compositon (called '''isometry group''').

Partial isometry (2119 bytes)
1: In [[functional analysis]] a '''partial isometry''' is a linear map ''W'' between Hilbert spaces '...
3: Any [[unitary operator]] on ''H'' is a partial isometry with initial and subspaces being all of ''H''.
9: is a partial isometry with initial subspace
17: ...l complement of ''H''₁. Thus a partial isometry is also sometimes defined as a closed partially d...
19: ...re projections. This allows us to define partial isometry in any C*-algebra as follows:

Glide reflection (1303 bytes)
2: ...ometry]], a '''glide reflection''' is a type of [[isometry]] of the [[Euclidean plane]].
4: Within the [[isometry|isometry group]] of the plane, the product of a [[rotation...
6: For example, there is an isometry consisting of the reflection on the ''x''-axis, f...

Polar decomposition (1050 bytes)
1: ...lex Hilbert spaces as the product of a [[partial isometry]] and a non-negative self-adjoint operator. It g...
5: ...ded linear mapping then there is a unique partial isometry ''U'' defined on the closure of the range of |''T...
17: so there is an isometry ''U'' defined uniquely on the closure of the rang...

Eigenplane (1825 bytes)
5: ...tudied is that in which the linear operator is an isometry ''M'' of the [[hypersphere]] (written ''S<sup>3</...
13: ...g the angles of the eigenrotations of a candidate isometry for [[shape of the universe|topological lensing]]...

Killing vector field (1614 bytes)
1: ... fields are the [[infinitesimal generator]]s of [[isometry|isometries]]; that is, [[flow (geometry)|flow]]s ...
12: ...fields on ''M''. This is the Lie algebra of the [[isometry group]] of the manifold.

Euclidean group (2974 bytes)
1: ...lidean space]], it may also be described as the [[isometry]] group of the Euclidean [[metric]]. It has dimen...
7: ...f ''E''(''n''): for any translation ''t'' and any isometry ''u'', we have

Fuchsian group (2488 bytes)
1: ...icular type of [[group (mathematics)|group]] of [[isometry|isometries]] of the [[hyperbolic plane]]. A Fuchs...
13: ...up of all [[orientable|orientation-preserving]] [[isometry|isometries]] of ''H''.

Crystallographic group (542 bytes)
1: ...group]] of the [[group (mathematics)|group]] of [[isometry|isometries]] of some [[geometric space]] (typical...

Symmetric space (887 bytes)
5: ...ifold]] such that for every point there exists an isometry fixing that point and inducing minus the identity...

Chirality (mathematics) (3160 bytes)
3: ...ins at least one indirect (orientation reversing) isometry; see [[improper rotation]] for a discussion in [[...
11: ...hich is invariant under the orientation reversing isometry <math>(x,y,z)\mapsto(-y,x,-z)</math> and thus ach...

Word metric (805 bytes)
3: ...(or right) action of the group on itself to be an isometry.

Riemann sphere (2911 bytes)
35: ...the round [[metric tensor|metric]] the [[isometry|isometry group]] is the subgroup PSU₂ '''C''' (...

Unitary operator (820 bytes)
7: * ''U'' is a [[surjective]] [[isometry]]

Locally (975 bytes)
1: ...e (e.g., [[homeomorphism]], [[diffeomorphism]], [[isometry]]) between

Real tree (1095 bytes)
2: ...t ''f(a)=x'' and ''f(b)=y,'' and this arc is an [[isometry|isometric]] [[embedding]].

Glossary of Riemannian and metric geometry (10196 bytes)
25: '''Arc-wise isometry''' the same as ''path isometry''.
107: '''[[Isometry]]'''
162: '''[[Isometry|Path isometry]]'''
170: ...''' A map <math>f:X\to Y</math> is called a quasi-isometry if there is a constant ''C'' such that ''f''(''X...
172: ...e any map between compact metric spaces is a quasiisometry.

Frieze group (4723 bytes)
1: ...ngle). The elements of the group are therefore [[isometry|isometries]] of the plane, or of a strip. As wit...
20: ...ines. The elements in this group correspond to [[isometry|isometries]] (or equivalently, [[bijection|biject...

Uniformization theorem (1088 bytes)
3: ...of a [[discrete group|discrete subgroup]] of an [[isometry group]]:

Improper rotation (1487 bytes)
13: [[Isometry]], [[Orthogonal group]]

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