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- An isometry of the hyperbolic plane is a mapping of the hyperbolic plane to itself that preserves the underlying hyperbolic geometry, such as distances and angles1. The isometries of the hyperbolic plane form a group under composition1. An isometry of the hyperbolic plane can be either orientation-preserving or orientation-reversing1. An isometry of hyperbolic n-space is an element of O(n, 1)2.Learn more:✕This summary was generated using AI based on multiple online sources. To view the original source information, use the "Learn more" links.An isometry of the hyperbolic plane is a mapping of the hyperbolic plane to itself that preserves the underlying hyperbolic geometry (e.g. distances and angles). The isometries of the hyperbolic plane form a group under composition. An isometry of the hyperbolic plane can be either orientation-preserving or orientation-reversing.encycla.com/Hyperbolic_plane_isometryAn isometry of hyperbolic n-space is an element of O(n, 1). This is the group of matrices which preserve the quadratic form (+++...++−) which n +’s and 1 −.www3.math.tu-berlin.de/geometrie/Lehre/WS05/Ge…
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