RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2000, Volume 191, Number 5, Pages 39–66 (Mi msb476)  

This article is cited in 10 scientific papers (total in 10 papers)

The problem of constructive equivalence in differential geometry

B. M. Dubrov, B. P. Komrakov

International Center "Sophus Lie"

Abstract: The present paper is devoted to the algorithmic construction of diffeomorphisms establishing the equivalence of geometric structures. For structures of finite type the problem reduces to integration of completely integrable distributions with a known symmetry algebra and further to integration of Maurer–Cartan forms. We develop algorithms that reduce this problem to integration of closed 1-forms and equations of Lie type that are characterized by the fact that they admit a non-linear superposition principle. As an application we consider the problem of constructive equivalence for the structures of absolute parallelism and for the transitive Lie algebras of vector fields on manifolds.

DOI: https://doi.org/10.4213/sm476

Full text: PDF file (384 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:5, 655–681

Bibliographic databases:

UDC: 514.76
MSC: Primary 53A55; Secondary 17B66, 22E60, 34A26, 53C05, 53C10, 58A10, 58A20, 5
Received: 31.05.1999

Citation: B. M. Dubrov, B. P. Komrakov, “The problem of constructive equivalence in differential geometry”, Mat. Sb., 191:5 (2000), 39–66; Sb. Math., 191:5 (2000), 655–681

Citation in format AMSBIB
\Bibitem{DubKom00}
\by B.~M.~Dubrov, B.~P.~Komrakov
\paper The problem of constructive equivalence in differential geometry
\jour Mat. Sb.
\yr 2000
\vol 191
\issue 5
\pages 39--66
\mathnet{http://mi.mathnet.ru/msb476}
\crossref{https://doi.org/10.4213/sm476}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1773768}
\zmath{https://zbmath.org/?q=an:0969.53012}
\transl
\jour Sb. Math.
\yr 2000
\vol 191
\issue 5
\pages 655--681
\crossref{https://doi.org/10.1070/sm2000v191n05ABEH000476}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000089654100003}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-0034341442}


Linking options:
  • http://mi.mathnet.ru/eng/msb476
  • https://doi.org/10.4213/sm476
  • http://mi.mathnet.ru/eng/msb/v191/i5/p39

    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
    Erratum

    This publication is cited in the following articles:
    1. Fels, ME, “Integrating scalar ordinary differential equations with symmetry revisited”, Foundations of Computational Mathematics, 7:4 (2007), 417  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Ian. M. Anderson, Mark E. Fels, “The Cauchy Problem for Darboux Integrable Systems and Non-Linear d'Alembert Formulas”, SIGMA, 9 (2013), 017, 22 pp.  mathnet  crossref  mathscinet
    3. Peter J. Vassiliou, “Cauchy Problem for a Darboux Integrable Wave Map System and Equations of Lie Type”, SIGMA, 9 (2013), 024, 21 pp.  mathnet  crossref  mathscinet
    4. J.N.. Clelland, P.J.. Vassiliou, “A solvable string on a Lorentzian surface”, Differential Geometry and its Applications, 2013  crossref  mathscinet  isi  scopus  scopus  scopus
    5. Doubrov B., Kruglikov B., “On the Models of Submaximal Symmetric Rank 2 Distributions in 5D”, Differ. Geom. Appl., 35:1 (2014), 314–322  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Catalano Ferraioli D., de Oliveira Silva L.A., “Second order evolution equations which describe pseudospherical surfaces”, J. Differ. Equ., 260:11 (2016), 8072–8108  crossref  mathscinet  zmath  isi  scopus
    7. Fels M.E., “on the Construction of Simply Connected Solvable Lie Groups”, J. Lie Theory, 27:1 (2017), 193–215  mathscinet  zmath  isi
    8. De Dona J., Tehseen N., Vassiliou P.J., “Symmetry Reduction, Contact Geometry, and Partial Feedback Linearization”, SIAM J. Control Optim., 56:1 (2018), 201–230  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    9. Campoamor-Stursberg R., “Reduction By Invariants and Projection of Linear Representations of Lie Algebras Applied to the Construction of Nonlinear Realizations”, J. Math. Phys., 59:3 (2018), 033502  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. Vassiliou P.J., “Cascade Linearization of Invariant Control Systems”, J. Dyn. Control Syst., 24:4 (2018), 593–623  crossref  mathscinet  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:426
    Full text:113
    References:45
    First page:1

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