Short geodesics for Ad invariant metrics in locally exponential Lie groups

  • Piotr Kielanowski
  • Anatol Odzijewicz
  • Emma Previato
Conference paper
Part of the Trends in Mathematics book series (TM)


We study the geodesic structure of Lie groups K that admit biinvariant metrics: the main results concern the fact that one-parameter groups are short paths for those metrics, as in the Riemannian case.


Lie group Banach space Finsler metric bi-invariant metric geodesic one-parameter group isometry group unitary group. 

Mathematics Subject Classification (2000)

Primary 22E65 58B20 Secondary 53C22 47B10 58D05. 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Piotr Kielanowski
    • 1
  • Anatol Odzijewicz
    • 2
  • Emma Previato
    • 3
  1. 1.Departamento de FísicaCINVESTAVCiudad de MéxicoMexico
  2. 2.Institute of MathematicsUniversity of BialystokBialystokPoland
  3. 3.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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