Counting geodesics on compact Lie groups

Autor(es)

Seco, Lucas ^[1] ; San Martin, Luiz A. B. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Brasilia UnB, Dept Matemat, Campus Darcy Ribeiro, Brasilia, DF - Brazil

^[2] Univ Campinas UNICAMP, Dept Matemat, Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS; v. 56, p. 325-343, FEB 2018.
• Citações Web of Science: 0

Resumo

We count the geodesics of a given length connecting two points of a compact connected Lie group with a biinvariant metric. We reduce the question to the maximal torus by using the lattice, the diagram and the Weyl group to count the geodesics that occur outside the maximal torus. We apply our results to give short proofs of known results on conjugate and cut points of compact semisimple Lie groups. (C) 2017 Elsevier B.V. All rights reserved. (AU)

• Processo FAPESP: 07/06896-5 - Geometria de sistemas de controle, sistemas dinâmicos e estocásticos
• Beneficiário: Luiz Antonio Barrera San Martin
• Modalidade de apoio: Auxílio à Pesquisa - Temático