Abstract
Let M be a compact Lie group. The invariant scalar product (•, •) in the Lie algebra M = T Id M defines a left-invariant Riemannian structure on M:
So in every tangent space T q M there is a scalar product (•,•)q. For any Lipschitzian curve
its Riemannian length is defined as integral of velocity:
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© 2004 Springer-Verlag Berlin Heidelberg
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Agrachev, A.A., Sachkov, Y.L. (2004). Examples of Optimal Control Problems on Compact Lie Groups. In: Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06404-7_19
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DOI: https://doi.org/10.1007/978-3-662-06404-7_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05907-0
Online ISBN: 978-3-662-06404-7
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