caa a22 4500 605496617 CHVBK 20210128100537.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10231-013-0379-x doi (NATIONALLICENCE)springer-10.1007/s10231-013-0379-x The equivalence problem of curves in a Riemannian manifold [Elektronische Daten] [M. Castrillón López, V. Fernández Mateos, J. Muñoz Masqué] The equivalence problem of curves with values in a Riemannian manifold is solved. The domain of validity of Frenet's theorem is shown to be the spaces of constant curvature. For a general Riemannian manifold, new invariants must thus be added. There are two important generic classes of curves: namely Frenet curves and a new class called curves "in normal position”. They coincide in dimensions $$\le 4$$ ≤ 4 only. A sharp bound for asymptotic stability of differential invariants is obtained, the complete systems of invariants are characterized, and a procedure of generation is presented. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 Asymptotic stability nationallicence Complete systems of invariants nationallicence Congruence nationallicence Curvatures of a curve nationallicence Differential invariant nationallicence Frenet frame nationallicence Isometry nationallicence Killing vector field nationallicence Levi-Civita connection nationallicence Normal general position nationallicence Riemannian metric nationallicence Castrillón López M. Departamento de Geometría y Topología Facultad de Matemáticas, UCM, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Avda. Complutense s/n, 28040, Madrid, Spain aut Fernández Mateos V. Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain aut Muñoz Masqué J. Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain aut Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/2(2015-04-01), 343-367 0373-3114 194:2<343 2015 194 10231 https://doi.org/10.1007/s10231-013-0379-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-013-0379-x text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Castrillón López M. Departamento de Geometría y Topología Facultad de Matemáticas, UCM, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Avda. Complutense s/n, 28040, Madrid, Spain aut NATIONALLICENCE 700 1- Fernández Mateos V. Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain aut NATIONALLICENCE 700 1- Muñoz Masqué J. Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/2(2015-04-01), 343-367 0373-3114 194:2<343 2015 194 10231