RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



SIGMA:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


SIGMA, 2012, Volume 8, 059, 17 pages (Mi sigma736)  

This article is cited in 1 scientific paper (total in 1 paper)

Formal integrability for the nonautonomous case of the inverse problem of the calculus of variations

Oana Constantinescu

Faculty of Mathematics, Alexandru Ioan Cuza University, Bd. Carol no. 11, 700506, Iasi, Romania

Abstract: We address the integrability conditions of the inverse problem of the calculus of variations for time-dependent SODE using the Spencer version of the Cartan–Kähler theorem. We consider a linear partial differential operator $P$ given by the two Helmholtz conditions expressed in terms of semi-basic 1-forms and study its formal integrability. We prove that $P$ is involutive and there is only one obstruction for the formal integrability of this operator. The obstruction is expressed in terms of the curvature tensor $R$ of the induced nonlinear connection. We recover some of the classes of Lagrangian semisprays: flat semisprays, isotropic semisprays and arbitrary semisprays on 2-dimensional manifolds.

Keywords: formal integrability; partial differential operators; Lagrangian semisprays; Helmholtz conditions.

DOI: https://doi.org/10.3842/SIGMA.2012.059

Full text: PDF file (453 kB)
Full text: http://emis.mi.ras.ru/.../059
References: PDF file   HTML file

Bibliographic databases:

ArXiv: 1203.1716
MSC: 49N45; 58E30; 34A26; 37J30
Received: March 16, 2012; in final form September 3, 2012; Published online September 6, 2012
Language:

Citation: Oana Constantinescu, “Formal integrability for the nonautonomous case of the inverse problem of the calculus of variations”, SIGMA, 8 (2012), 059, 17 pp.

Citation in format AMSBIB
\Bibitem{Con12}
\by Oana Constantinescu
\paper Formal integrability for the nonautonomous case of the inverse problem of the calculus of variations
\jour SIGMA
\yr 2012
\vol 8
\papernumber 059
\totalpages 17
\mathnet{http://mi.mathnet.ru/sigma736}
\crossref{https://doi.org/10.3842/SIGMA.2012.059}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2970769}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000308736800001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84867025865}


Linking options:
  • http://mi.mathnet.ru/eng/sigma736
  • http://mi.mathnet.ru/eng/sigma/v8/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. Bucataru I. Constantinescu O., “Generalized Helmholtz Conditions For Non-Conservative Lagrangian Systems”, Math. Phys. Anal. Geom., 18:1 (2015), 25  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
    Number of views:
    This page:238
    Full text:32
    References:24

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019