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ArticleOriginal scientific text

Title

A note on generalized flag structures

Authors 1

Affiliations

  1. Institute of Mathematics, Pedagogical University, Rejtana 16 A, 35-310 Rzeszów, Poland

Abstract

Generalized flag structures occur naturally in modern geometry. By extending Stefan's well-known statement on generalized foliations we show that such structures admit distinguished charts. Several examples are included.

Keywords

ENG
generalized foliation, subfoliation, flag structure, distinguished chart

Bibliography

  1. M. Bauer, Feuilletage singulier défini par une distribution presque régulière, Thèse, Univ. Louis Pasteur (Strasbourg), Publ. I.R.M.A., 1985.
  2. P. Dazord, Feuilletages à singularités, Indag. Math. 47 (1985), 21-39.
  3. P. Dazord, A. Lichnerowicz et C. M. Marle, Structure locale des variétés de Jacobi, J. Math. Pures Appl. 70 (1991), 101-152.
  4. R. Ibáñez, M. de León, J. C. Marrero and D. Martin de Diego, Dynamics of generalized Poisson and Nambu-Poisson brackets, J. Math. Phys. 38 (1997), 2332-2344.
  5. R. Ibáñez, M. de León, J. C. Marrero and E. Padrón, Nambu-Jacobi and generalized Jacobi manifolds, preprint, 1997.
  6. C. M. Marle, Lie group actions on a canonical manifold, in: Symplectic Geometry, A. Crumeyrolle and J. Grifone (eds.), Pitman, Boston, 1983, 144-166.
  7. P. W. Michor and A. M. Vinogradov, n-ary Lie and associative algebras, preprint ESI 402, 1996.
  8. P. W. Michor and C. Vizman, n-transitivity of certain diffeomorphism groups, Acta Math. Univ. Comenian. 63 (1994), 221-225.
  9. P. Molino, Riemannian Foliations, Progr. Math. 73, Birkhäuser, 1988.
  10. P. Molino, Orbit-like foliations, in: Geometric Study of Foliations (Tokyo, 1993), World Sci., Singapore, 1994, 97-119.
  11. R. Ouzilou, Hamiltonian actions on Poisson manifolds, in: Symplectic Geometry, A. Crumeyrolle and J. Grifone (eds.), Pitman, Boston, 1983, 172-183.
  12. T. Rybicki, Pseudo-n-transitivity of the automorphism group of a geometric structure, Geom. Dedicata 67 (1997), 181-186.
  13. P. Stefan, Accessibility and foliations with singularities, Bull. Amer. Math. Soc. 80 (1974), 1142-1145.
  14. P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713.
  15. H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188.
  16. I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progr. Math. 118, Birkhäuser, Basel, 1994.
  17. V. P. Vilflyantsev, Frobenius theorem for differential systems with singularities, Vestnik Moskov. Univ. 3 (1980), 11-14 (in Russian).
  18. R. A. Wolak, Characteristic classes of almost-flag structures, Geom. Dedicata 24 (1987), 207-220.
Annales Polonici Mathematici
1998/69/1
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Pages:
89-97
Main language of publication
English
Received
1997-12-11
Published
1998
Exact and natural sciences