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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