Finite-type integrable geometric structures |
| |
Authors: | V A Yumaguzhin |
| |
Institution: | (1) Mathematical Institute, Silesian University in Opava, Opava, Czech Republic |
| |
Abstract: | In this paper, we consider finite-type geometric structures of arbitrary order and solve the integrability problem for these
structures. This problem is equivalent to the integrability problem for the corresponding G-structures. The latter problem is solved by constructing the structure functions for G-structures of order ≥1. These functions coincide with the well-known ones for the first-order G-structures, although their constructions are different. We prove that a finite-type G-structure is integrable if and only if the structure functions of the corresponding number of its first prolongations are
equal to zero. Applications of this result to second-and third-order ordinary differential equations are noted.
__________
Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 10, No. 1, Geometry
of Integrable Models, 2004. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|