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dc.contributor.author
Salvai, Marcos Luis
dc.date.available
2024-09-11T10:57:00Z
dc.date.issued
2024-02
dc.identifier.citation
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
dc.identifier.issn
0046-5755
dc.identifier.uri
http://hdl.handle.net/11336/244049
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
SCREW MOTION
dc.subject
LENGTH SPECTRUM
dc.subject
COMPLEX LENGTH SPECTRUM
dc.subject
HYPERBOLIC 3-MANIFOLD
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
The sub-Riemannian length spectrum for screw motions of constant pitch on flat and hyperbolic 3-manifolds
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2024-09-10T12:56:40Z
dc.journal.volume
218
dc.journal.number
2
dc.journal.pagination
1-20
dc.journal.pais
Alemania
dc.description.fil
Fil: Salvai, Marcos Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina
dc.journal.title
Geometriae Dedicata
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s10711-024-00896-1
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s10711-024-00896-1
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