Open AccessGeodesic flow on the diffeomorphism group of the circle
Author(s) -
Adrian Constantin,
Boris Kolev
Publication year - 2003
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/s00014-003-0785-6
Subject(s) - diffeomorphism , mathematics , exponential map (riemannian geometry) , geodesic , geodesic map , lie group , group (periodic table) , pure mathematics , invariant (physics) , riemannian geometry , exponential function , mathematical analysis , geometry , scalar curvature , sectional curvature , mathematical physics , curvature , organic chemistry , chemistry
We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds