Counting geodesics on compact symmetric spaces

Autor:	Seco, Lucas, Patrão, Mauro
Rok vydání:	2022
Předmět:	Mathematics - Differential Geometry Primary: 53C22 53C35 Secondary: 53C20
Druh dokumentu:	Working Paper
Popis:	We describe the inverse image of the Riemannian exponential map at a basepoint of a compact symmetric space as the disjoint union of so called focal orbits through a maximal torus. These are orbits of a subgroup of the isotropy group acting in the tangent space at the basepoint. We show how their dimensions (infinitesimal data) and connected components (topological data) are encoded in the diagram, multiplicities, Weyl group and lattice of the symmetric space. Obtaining this data is precisely what we mean by counting geodesics. This extends previous results on compact Lie groups. We apply our results to give short independent proofs of known results on compact symmetric spaces. Comment: 1 figure
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2204.11984 Zobrazit plný text záznamu View this record from Arxiv