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.
@article{bwmeta1.element.bwnjournal-article-apmv69z1p89bwm, author = {Tomasz Rybicki}, title = {A note on generalized flag structures}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {89-97}, zbl = {0978.57024}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p89bwm} }
Tomasz Rybicki. A note on generalized flag structures. Annales Polonici Mathematici, Tome 69 (1998) pp. 89-97. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z1p89bwm/
[000] [1] M. Bauer, Feuilletage singulier défini par une distribution presque régulière, Thèse, Univ. Louis Pasteur (Strasbourg), Publ. I.R.M.A., 1985. | Zbl 0657.58005
[001] [2] P. Dazord, Feuilletages à singularités, Indag. Math. 47 (1985), 21-39. | Zbl 0584.57016
[002] [3] P. Dazord, A. Lichnerowicz et C. M. Marle, Structure locale des variétés de Jacobi, J. Math. Pures Appl. 70 (1991), 101-152. | Zbl 0659.53033
[003] [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. | Zbl 0878.58024
[004] [5] R. Ibáñez, M. de León, J. C. Marrero and E. Padrón, Nambu-Jacobi and generalized Jacobi manifolds, preprint, 1997.
[005] [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.
[006] [7] P. W. Michor and A. M. Vinogradov, n-ary Lie and associative algebras, preprint ESI 402, 1996.
[007] [8] P. W. Michor and C. Vizman, n-transitivity of certain diffeomorphism groups, Acta Math. Univ. Comenian. 63 (1994), 221-225.
[008] [9] P. Molino, Riemannian Foliations, Progr. Math. 73, Birkhäuser, 1988.
[009] [10] P. Molino, Orbit-like foliations, in: Geometric Study of Foliations (Tokyo, 1993), World Sci., Singapore, 1994, 97-119.
[010] [11] R. Ouzilou, Hamiltonian actions on Poisson manifolds, in: Symplectic Geometry, A. Crumeyrolle and J. Grifone (eds.), Pitman, Boston, 1983, 172-183. | Zbl 0514.58010
[011] [12] T. Rybicki, Pseudo-n-transitivity of the automorphism group of a geometric structure, Geom. Dedicata 67 (1997), 181-186. | Zbl 0896.58014
[012] [13] P. Stefan, Accessibility and foliations with singularities, Bull. Amer. Math. Soc. 80 (1974), 1142-1145. | Zbl 0293.57015
[013] [14] P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713. | Zbl 0342.57015
[014] [15] H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 180 (1973), 171-188. | Zbl 0274.58002
[015] [16] I. Vaisman, Lectures on the Geometry of Poisson Manifolds, Progr. Math. 118, Birkhäuser, Basel, 1994.
[016] [17] V. P. Vilflyantsev, Frobenius theorem for differential systems with singularities, Vestnik Moskov. Univ. 3 (1980), 11-14 (in Russian).
[017] [18] R. A. Wolak, Characteristic classes of almost-flag structures, Geom. Dedicata 24 (1987), 207-220. | Zbl 0682.57008