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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 2, Pages 151–192 (Mi izv1049)  

This article is cited in 3 scientific papers (total 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 $s\geq k$ 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.)

DOI: https://doi.org/10.4213/im1049

Full text: PDF file (802 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:2, 345–382

Bibliographic databases:

UDC: 514.763
MSC: 53A55
Received: 10.04.2006

Citation: R. A. Sarkisyan, I. G. Shandra, “Regularity and Tresse's theorem for geometric structures”, Izv. RAN. Ser. Mat., 72:2 (2008), 151–192; Izv. Math., 72:2 (2008), 345–382

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Kruglikov B., “Point Classification of Second Order ODEs: Tresse Classification Revisited and Beyond”, Differential Equations: Geometry, Symmetries and Integrability - the Abel Symposium 2008, Abel Symposia, 5, 2009, 199–221  mathscinet  zmath  isi
    2. R. A. Sarkisyan, “Rationality of the Poincaré series in Arnold's local problems of analysis”, Izv. Math., 74:2 (2010), 411–438  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Kruglikov B., Lychagin V., “Global Lie–Tresse theorem”, Sel. Math.-New Ser., 22:3 (2016), 1357–1411  crossref  mathscinet  zmath  isi  elib  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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