RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
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



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






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


Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 6, Pages 173–222 (Mi izv368)  

This article is cited in 2 scientific papers (total in 2 papers)

Monge–Ampére equations and characteristic connection functors

D. V. Tunitsky

International Center "Sophus Lie"

Abstract: We investigate contact equivalence of Monge–Ampére equations. We define a category of Monge–Ampére equations and introduce the notion of a characteristic connection functor. This functor maps the category of Monge–Ampére equations to the category of affine connections. We give a constructive description of the characteristic connection functors corresponding to three subcategories, which include a large class of Monge–Ampére equations of elliptic and hyperbolic type. This essentially reduces the contact equivalence problem for Monge–Ampére equations in the cases under study to the equivalence problem for affine connections. Using E. Cartan's familiar theory, we are thus able to state and prove several criteria of contact equivalence for a large class of elliptic and hyperbolic Monge–Ampére equations.

DOI: https://doi.org/10.4213/im368

Full text: PDF file (3928 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2001, 65:6, 1243–1290

Bibliographic databases:

MSC: 53B05, 58A17
Received: 01.12.1999

Citation: D. V. Tunitsky, “Monge–Ampére equations and characteristic connection functors”, Izv. RAN. Ser. Mat., 65:6 (2001), 173–222; Izv. Math., 65:6 (2001), 1243–1290

Citation in format AMSBIB
\Bibitem{Tun01}
\by D.~V.~Tunitsky
\paper Monge--Amp\'ere equations and characteristic connection functors
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 6
\pages 173--222
\mathnet{http://mi.mathnet.ru/izv368}
\crossref{https://doi.org/10.4213/im368}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1892907}
\zmath{https://zbmath.org/?q=an:1022.58009}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 6
\pages 1243--1290
\crossref{https://doi.org/10.1070/IM2001v065n06ABEH000368}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746718139}


Linking options:
  • http://mi.mathnet.ru/eng/izv368
  • https://doi.org/10.4213/im368
  • http://mi.mathnet.ru/eng/izv/v65/i6/p173

    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. Marvan, M, “Differential invariants of generic hyperbolic Monge-Ampere equations”, Central European Journal of Mathematics, 5:1 (2007), 105  crossref  mathscinet  zmath  isi  scopus
    2. D. V. Tunitsky, “Monge–Ampère equations and tensorial functors”, Izv. Math., 73:6 (2009), 1217–1263  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:243
    Full text:97
    References:53
    First page:1

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