3RD-ORDER ORDINARY DIFFERENTIAL-EQUATIONS AND LEGENDRE CONNECTIONS

Authors
SATO H YOSHIKAWA AY
Citation
H. Sato et Ay. Yoshikawa, 3RD-ORDER ORDINARY DIFFERENTIAL-EQUATIONS AND LEGENDRE CONNECTIONS, Journal of the Mathematical Society of Japan, 50(4), 1998, pp. 993-1013
Citations number
10
Categorie Soggetti
Mathematics,Mathematics
Journal title
Journal of the Mathematical Society of Japan → ACNP
ISSN journal
00255645
Volume
50
Issue
4
Year of publication
1998
Pages
993 - 1013
Database
ISI
SICI code
0025-5645(1998)50:4<993:3ODALC>2.0.ZU;2-C
Abstract
We use N. Tanaka's theory of normal Cartan connections associated with simple graded Lie algebras to study Cartan's equivalence problem of s ingle third order ordinary differential equations under contact transf ormations. As: a result we obtain the complete structure equation with two differential invariants, which is applied on general Legendre Gra ssmann bundles of three-dimensional contact manifolds.