This article is cited in 3 papers

Regularity and Tresse's theorem for geometric structures

R. A. Sarkisyan, I. G. Shandra

Finance Academy under the Government of the Russian Federation

Abstract: For any non-special bundle $P\to X$ of geometric structures we prove that the $k$-jet space $J^k$ of this bundle with an appropriate $k$ contains an open dense domain $U_k$ on which Tresse's theorem holds. For every $s\geqslant k$ we prove that the pre-image $\pi^{-1}(k,s)(U_k)$ of $U_k$ under the natural projection $\pi(k,s)\colon J^s\to J^k$ consists of regular points. (A point of $J^s$ is said to be regular if the orbits of the group of diffeomorphisms induced from $X$ have locally constant dimension in a neighbourhood of this point.)

UDC: 514.763

MSC: 53A55

Received: 10.04.2006

DOI: 10.4213/im1049

 English version: Izvestiya: Mathematics, 2008, 72:2, 345–382

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