The equivalence problem of curves in a Riemannian manifold
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| 024 | 7 | 0 | |a 10.1007/s10231-013-0379-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10231-013-0379-x | ||
| 245 | 0 | 4 | |a The equivalence problem of curves in a Riemannian manifold |h [Elektronische Daten] |c [M. Castrillón López, V. Fernández Mateos, J. Muñoz Masqué] |
| 520 | 3 | |a 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. | |
| 540 | |a Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2013 | ||
| 690 | 7 | |a Asymptotic stability |2 nationallicence | |
| 690 | 7 | |a Complete systems of invariants |2 nationallicence | |
| 690 | 7 | |a Congruence |2 nationallicence | |
| 690 | 7 | |a Curvatures of a curve |2 nationallicence | |
| 690 | 7 | |a Differential invariant |2 nationallicence | |
| 690 | 7 | |a Frenet frame |2 nationallicence | |
| 690 | 7 | |a Isometry |2 nationallicence | |
| 690 | 7 | |a Killing vector field |2 nationallicence | |
| 690 | 7 | |a Levi-Civita connection |2 nationallicence | |
| 690 | 7 | |a Normal general position |2 nationallicence | |
| 690 | 7 | |a Riemannian metric |2 nationallicence | |
| 700 | 1 | |a Castrillón López |D M. |u Departamento de Geometría y Topología Facultad de Matemáticas, UCM, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Avda. Complutense s/n, 28040, Madrid, Spain |4 aut | |
| 700 | 1 | |a Fernández Mateos |D V. |u Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain |4 aut | |
| 700 | 1 | |a Muñoz Masqué |D J. |u Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain |4 aut | |
| 773 | 0 | |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 343-367 |x 0373-3114 |q 194:2<343 |1 2015 |2 194 |o 10231 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10231-013-0379-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10231-013-0379-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Castrillón López |D M. |u Departamento de Geometría y Topología Facultad de Matemáticas, UCM, Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Avda. Complutense s/n, 28040, Madrid, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Fernández Mateos |D V. |u Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Muñoz Masqué |D J. |u Instituto de Seguridad de la Información, CSIC, C/ Serrano 144, 28006, Madrid, Spain |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Annali di Matematica Pura ed Applicata (1923 -) |d Springer Berlin Heidelberg |g 194/2(2015-04-01), 343-367 |x 0373-3114 |q 194:2<343 |1 2015 |2 194 |o 10231 | ||