NDLI: The equivalence problem of curves in a Riemannian manifold

Content Provider	Springer Nature Link
Author	Castrillón López, M. Fernández Mateos, V. Muñoz Masqué, J.
Copyright Year	2013
Abstract	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 $$\le 4$$ 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.
Ending Page	367
Page Count	25
Starting Page	343
File Format	PDF
ISSN	03733114
e-ISSN	16181891
Journal	Annali di Matematica Pura ed Applicata
Issue Number	2
Volume Number	194
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2013-09-29
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Isometry Congruence Riemannian metric Curvatures of a curve Local Riemannian geometry Killing vector field Normal general position Mathematics Levi-Civita connection Symmetric spaces Asymptotic stability Frenet frame Methods of Riemannian geometry Differential invariant Jets Complete systems of invariants Differential invariants (local theory), geometric objects Curves in Euclidean space
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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