Lie Groups pp 94-106 | Cite as

Geodesics and Maximal Tori

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)


An important theorem of Cartan asserts that any two maximal tori in a compact Lie group are conjugate. We will give two proofs of this, one using some properties of geodesics in a Riemannian manifold and one using some algebraic topology. The reader will experience no loss of continuity if he reads one of these proofs and skips the other. The proof in this chapter is simpler and more self-contained.


Riemannian Manifold Maximal Torus Unit Tangent Vector Geodesic Curve Linear Fractional Transformation 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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