FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2004, VOLUME 10, NUMBER 1, PAGES 255-269

Finite-type integrable geometric structures

V. A. Yumaguzhin

Abstract

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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 $$³ 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.

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Last modified: October 25, 2004