Abstract
In this chapter we will first introduce the isometries of \( {\text{R}}^{ 4} \) and \( {\text{R}}^{ 3, 1} \) and connect them with the corresponding principal axis theorem. Then we aim to understand how these isometries act in \( {\text{S}}^{ 3} \) and \( {\text{H}}^{ 3} \).
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© 2012 Florin Diacu
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Diacu, F. (2012). Isometric Rotations. In: Relative Equilibria of the Curved N-Body Problem. Atlantis Series in Dynamical Systems, vol 1. Atlantis Press, Paris. https://doi.org/10.2991/978-94-91216-68-8_4
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DOI: https://doi.org/10.2991/978-94-91216-68-8_4
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Publisher Name: Atlantis Press, Paris
Print ISBN: 978-94-91216-67-1
Online ISBN: 978-94-91216-68-8
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