...dentified boundaries are isometric and identification is carried out by an isometry (cf. [[Isometric mapping|Isometric mapping]]). The distance between two poi
3 KB (397 words) - 15:04, 10 April 2023
...the helicoid is isometric to the [[Catenoid|catenoid]]. In fact such local isometry can be achieved as endpoint of a continuous one-parameter family of isometr
2 KB (310 words) - 19:56, 12 November 2023
is a linear [[Isometric mapping|isometric mapping]] (linear isometry) of $ A $
is an algebra isometry of $ A $
8 KB (1,167 words) - 11:37, 12 January 2021
...h point $p\in M$ is an isolated fixed point of some holomorphic involutory isometry $s_p$ of $M$. The component of the identity of the group $G$ of holomorphic
2 KB (388 words) - 23:00, 12 December 2020
This form is independent (apart from an isometry) of the choice of the Witt decomposition of $ V $.
anisotropic. Moreover, the isometry classes of $ ( V _ {t} , q _ {t} ) $,
8 KB (1,152 words) - 08:29, 6 June 2020
of which is an isolated fixed point of some involutory isometry $ S _ {p} $
...simply-connected irreducible globally symmetric Riemannian spaces up to an isometry is equivalent to the classification of irreducible orthogonal symmetric Lie
9 KB (1,321 words) - 19:42, 5 June 2020
this fact is a generalization of the isometry of a horosphere in Lobachevskii space to a Euclidean space.
4 KB (614 words) - 08:13, 6 June 2020
Up to an isometry there exists a unique complete simply-connected $n$-dimensional Riemannian
4 KB (626 words) - 05:24, 29 May 2016
...c domain $D$ in a complex Banach space there exists a unique (up to linear isometry) $\operatorname{JB} ^ { * }$-triple $E$ whose open unit ball is biholomorph
A bijective linear operator between $\operatorname{JB} ^ { * }$-triples is an isometry if and only if it respects the Jordan triple product.
10 KB (1,477 words) - 06:10, 26 March 2024
...ncyclopediaofmath.org/legacyimages/b/b110/b110090/b11009041.png" /> is the
isometry group of <img align="absmiddle" border="0" src="https://www.encyclopediaofm
10 KB (1,395 words) - 06:44, 9 October 2016
along curves on the base is an isometry of the fibres as unitary spaces. For every Hermitian metric there is a conn
4 KB (681 words) - 03:41, 21 March 2022
...y, also (b) implies (a), which involves a Borel isomorphism (rather than isometry or homeomorphism) between two metric spaces.
5 KB (655 words) - 20:33, 18 February 2012
...eodesic and the mapping $\psi : ( u , v ) \rightarrow ( 2 u , 2 v )$ is an isometry (cf. also [[Isometric mapping|Isometric mapping]]). Defining $x \sim y$ as
4 KB (606 words) - 19:47, 24 November 2023
...s the maximum of the $\dim(G(M, ds^2))$. For a description of the possible isometry groups of dimensions $\ge 2+(n-1)(n-2)/2$ cf. [[#References|[a2]]], [[#Refe
19 KB (2,034 words) - 04:04, 15 February 2024
...s spaces uniquely up to a piecewise-linear homeomorphism and even up to an isometry; on the other hand, by the topological invariance of the torsion, they also
4 KB (668 words) - 18:39, 13 January 2024
...the plane (axis) of the symmetry (see ). Any orthogonal transformation, or isometry, is the composite of a finite number of reflections.
6 KB (946 words) - 08:24, 6 June 2020
...encyclopediaofmath.org/legacyimages/r/r082/r082150/r08215057.png" /> is an
isometry, then for any point <img align="absmiddle" border="0" src="https://www.ency
....org/legacyimages/r/r082/r082150/r082150105.png" />; it turns out to be an
isometry and is called the Levi-Civita parallel displacement. The result of the tran
55 KB (7,564 words) - 16:56, 7 February 2011
where $\phi$ is an isometry with $\phi ^ { 2 } = \operatorname{id}$. Note that in dimension $m = 4$, th
5 KB (760 words) - 16:59, 1 July 2020
is a partial isometry (i.e. $ u ^ {*} u $
7 KB (1,052 words) - 08:06, 6 June 2020
is an isometry in the $ Q $-
7 KB (1,016 words) - 17:42, 13 January 2024