Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 25–28 | Cite as

Differential and Integral Projective Invariants for the Groups of Diffeomorphisms

  • P. V. Bibikov


In this paper we study the differential and integral invariants for the action of the projective group PGL(n + 1) on the group of diffeomorphisms Diff(ℝP n ) by conjugations. Cases n = 1 and n = 2 are considered. For n = 1 the algebra of differential invariants is found and the criterion of the local equivalence of two diffeomorphisms is obtained. Also several integral invariants for n = 1 and n = 2 are calculated, the analogy with Calaby integral invariant for the symplectic groups is established.

Keywords and phrases

Projective group action by conjugation jet space symmetry algebra differential invariant integral invariant 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Alekseevskii, A. Vinogradov, and V. Lychagin, Geometry I: Basic Ideas and Concepts of Differential Geometry, Vol. 1 of Encyclopaedia of Mathematical Sciences (Springer, Berlin, Heidelberg, 1991).CrossRefGoogle Scholar
  2. 2.
    V. Ovsienko and S. Tabachnikov, Projective Differential Geometry Old and New, from Schwarzian Derivative to the Cohomology of DiffeomorphismGroups, Vol. 165 of Cambridge Tracts in Mathematics (Cambridge Univ. Press, Cambridge, 2005).MATHGoogle Scholar
  3. 3.
    E. Calaby, “On the group of automorphisms of a symplictic manifold,” in Problems in Analysis, Lectures at the Symposium in Honor of S. Bochner (Princeton Univ. Press, Princeton, NJ, 1970), pp. 1–29.Google Scholar
  4. 4.
    E. Vinberg and V. Popov, Invariant Theory, Vol. 55 (VINITI, Moscow, 1989) [in Russian].MATHGoogle Scholar
  5. 5.
    N. Konovenko and V. Lychagin, “Invariants of projective actions and their applicationto recognition of fingerprints,” Anal.Math. Phys. 5 (3), 3–15 (2015).Google Scholar
  6. 6.
    E. Sharon and D. Mumford, “2D-shape analysis using conformal mapping,” Int. J. Comput. Vis. 70, 55–75 (2006).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Control SciencesMoscowRussia

Personalised recommendations