Metric geometry of infinite dimensional Lie groups and their homogeneous spaces

GABRIEL LAROTONDA

FORUM MATHEMATICUM

WALTER DE GRUYTER & CO

Lugar: Berlin; Año: 2019 vol. 31 p. 1567 - 1605

0933-7741

We study the geometry of Lie groups G with a continuous Finsler metric, in presence of a subgroup K such that the metric is right-invariant for the action of K. We present a systematic study of the metric and geodesic structure of homogeneous spaces M obtained by the quotient M≃G/K. Of particular interest are left-invariant metrics of G which are then bi-invariant for the action of K. We then focus on the geodesic structure of groups K that admit bi-invariant metrics, proving that one-parameter groups are short paths for those metrics, and characterizing all other short paths. We provide applications of the results obtained, in two settings: manifolds of Banach space linear operators, and groups of maps from compact manifolds.