Artículo
The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds
Fecha de publicación:
02/2024
Editorial:
Springer
Revista:
Geometriae Dedicata
ISSN:
0046-5755
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let M be an oriented three-dimensional Riemannian manifold of constant sectional curvature k = 0, 1, -1 and let SO (M) be its direct orthonormal frame bundle (direct refers to positive orientation), which maybe thought of as the set of all positions of a small body in M. Given lambda in R, there is a three-dimensional distribution D^lambda on SO (M) accounting for infinitesimal rototranslations of constant pitch lambda. When lambda is not k^2, there is a canonical sub-Riemannian structure on D^lambda. We present a geometric characterization of its geodesics, using a previous Lie theoretical description. For k = 0, -1 we compute the sub-Riemannian length spectrum of (SO(M),D^lambda) in terms of the complex length spectrum of M (given by the lengths and the holonomies of the periodic geodesics) when M has positive injectivity radius. In particular, for two complex length isospectral closed hyperbolic 3-manifolds (even if they are not isometric), the associated sub-Riemannian metrics on their direct orthonormal bundles are length isospectral.
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Articulos(CIEM)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Articulos de CENT.INV.Y ESTUDIOS DE MATEMATICA DE CORDOBA(P)
Citación
Salvai, Marcos Luis; The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds; Springer; Geometriae Dedicata; 218; 2; 2-2024; 1-20
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