Skip to main content
SpringerLink
Log in

r-Tuple almost product structures

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

A generalization of an almost product structure and an almost complex structure on smooth manifolds is constructed. The set of tensor differential invariants of type (2, 1) and the set of differential 2-forms for such structures are constructed. We show how these tensor invariants can be used to solve the classification problem for Monge–Ampère equations and Jacobi equations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. Cotton, “Sur les invariants différentiels de quelques équations linearies aux dérivées partielles du second ordre,” Ann. Sci. École Norm. Sup., 17, 211–244 (1900).

    MathSciNet  Google Scholar 

  2. A. G. Kushner, “Almost product structures and Monge–Ampère equations,” Lobachevskii J. Math., 23, 151–181 (2006), http://ljm.ksu.ru.

    MathSciNet  MATH  Google Scholar 

  3. A. G. Kushner, “A contact linearization problem for Monge–Ampère equations and Laplace invariants,” Acta Appl. Math., 101, No. 1–3, 177–189 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  4. A. G. Kushner, “Contact linearization of nondegenerate Monge–Ampère equations,” Russ. Math., 52, No. 4, 38–52 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  5. A. G. Kushner, “Classification of Monge–Ampère equations,” in: B. Kruglikov, V. Lychagin, and E. Straume, eds., Differential Equations: Geometry, Symmetries and Integrability. The Abel Symposium 2008. Proc. of the Fifth Abel Symposium on Differential Equations: Geometry, Symmetries and Integrability, June 18–21, 2008, Tromsø, Norway, Springer, Berlin (2009), pp. 223–256.

    Google Scholar 

  6. A. G. Kushner, “On contact equivalence of Monge–Ampère equations to linear equations with constant coefficients,” Acta Appl. Math., 109, No. 1, 197–210 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  7. A. G. Kushner, V. V. Lychagin, and V. N. Rubtsov, Contact Geometry and Nonlinear Differential Equations, Encyclopedia of Mathematics and Its Applications, Vol. 101, Cambridge Univ. Press, Cambridge (2007).

    MATH  Google Scholar 

  8. P. S. Laplace, “Recherches sur le calcul intégrals aux différences partielles,” Mémoires de l’Académie royale des Sciences de Paris (1773); Oeuvres complètes, Vol. 9, Gauthier-Villars, Paris (1893); New York (1966).

  9. S. Lie, “Über einige partielle Differential-Gleichungen zweiter Orduung,” Math. Ann., 5, 209–256 (1872).

    Article  MathSciNet  Google Scholar 

  10. S. Lie, “Begrundung einer Invarianten-Theorie der Beruhrungs-Transformationen,” Math. Ann., 8, 215–303 (1874).

    Article  MathSciNet  Google Scholar 

  11. V. V. Lychagin, Lectures on Geometry of Differential Equations, La Sapienza, Rome (1993).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Astrakhan State University, Institute of Control Sciences of RAS, Astrakhan, Russia

    A. G. Kushner

Authors
  1. A. G. Kushner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. G. Kushner.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 81–93, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kushner, A.G. r-Tuple almost product structures. J Math Sci 177, 569–578 (2011). https://doi.org/10.1007/s10958-011-0482-8

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-011-0482-8

Keywords

Search

Navigation