99:; transformations preserving this form are sometimes called "isometries", and the collection of them is then said to form an isometry group of the pseudo-Euclidean space.
258:
444:, World Scientific Lecture Notes in Physics, vol. 80 (2nd ed.), Hackensack, NJ: World Scientific Publishing Co. Pte. Ltd., p. 22,
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A discrete isometry group is an isometry group such that for every point of the space the set of images of the point under the isometries is a
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of objects/figures in the space, or functions defined on the space. See
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Automorphism group of a metric space or pseudo-Euclidean space
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of isometries. It represents in most cases a possible set of
62:. The elements of the isometry group are sometimes called
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Müller-Kirsten, Harald J. W.; Wiedemann, Armin (2010),
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Burago, Dmitri; Burago, Yuri; Ivanov, Sergei (2001),
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259:Fixed points of isometry groups in Euclidean space
229:are important cases where the isometry group is a
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116:consisting of the points of a
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287:Graduate Texts in Mathematics
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313:A course in metric geometry
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227:Riemannian symmetric spaces
206:of the hyperbolic plane is
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398:Classical invariant theory
202:The isometry group of the
187:The isometry group of the
168:The isometry group of the
108:The isometry group of the
361:10.1007/978-3-540-93816-3
204:Poincaré half-plane model
150:dihedral group of order 6
140:. A similar space for an
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407:10.1017/CBO9780511623660
97:isotropic quadratic form
44:distance-preserving maps
349:Berger, Marcel (1987),
283:Advanced Linear Algebra
213:The isometry group of
93:pseudo-Euclidean space
42:(that is, bijective,
142:equilateral triangle
48:function composition
189:Poincaré disc model
126:isosceles triangle
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60:identity function
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244:Point group
21:mathematics
265:References
75:symmetries
40:isometries
231:Lie group
37:bijective
482:Category
395:(1999),
281:(2008),
238:See also
208:PSL(2,R)
197:PSU(1,1)
110:subspace
103:Examples
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