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Geodesics in a Lie group

  1. Jun 3, 2015 #1
    Suppose to have a Lie group that is at the same time also a Riemannian manifold: is there a relation between Christoffel symbols and structure constants? What can i say about the geodesics in a Lie group? Do they have special properties?
  2. jcsd
  3. Jun 3, 2015 #2


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    It depends on what sort of metric the Lie group admits. This book seems to have a lot of the explanation that you need. Chapter 17 discusses metrics on Lie groups. If the metric is bi-invariant (see the text for the definition), then the geodesics correspond to the exponential map. Section 17.6 discusses Cartan connections, which can be defined when the metric is not bi-invariant, for which the geodesics coincide with integral curves of left-invariant vector fields.
  4. Jun 4, 2015 #3


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    Wow, "class notes" consisting of 807 pages. Some prof!
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