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http://yadda.icm.edu.pl:80/baztech/element/bwmeta1.element.baztech-article-PWA3-0011-0005

Czasopismo

Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics

Tytuł artykułu

On the leaves of a prefoliation of a K-differential space

Autorzy Piątkowski, A. 
Treść / Zawartość http://demmath.mini.pw.edu.pl/access.php https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
EN The definition of a prefoliation (M,F) of a K-differential space and the theorem about regularity of the inclusion of a leaf of a prefoliation are reminded. An example of a pair (M, F) of SC-differential spaces with the same set of points, which shows that even if the identity of .M is an immersion F -> M and (top M, top F) is a topological foliation in the sense of Ehresmann then (M, F) has not to be a prefoliation, is given. In the end, we show that if L is a proper leaf of a prefoliation (M, F) then the both structures of a K-differential spaces coincide on L.
Słowa kluczowe
PL przestrzeń różniczkowa   pole wektorowe  
EN differential space   vector fields   differential geometry  
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica. Warsaw Technical University Institute of Mathematics
Rocznik 2004
Tom Vol. 37, nr 3
Strony 689--696
Opis fizyczny Bibliogr. 11 poz.
Twórcy
autor Piątkowski, A.
  • Institute of Mathematics, Technical University of Łódź, Al. Politechnki 11, 90-924 Łódź, Poland, andpiat@p.lodz.pl
Bibliografia
[1] C. Ehresmann, Structures feuilletées, Proc. 5th Can. Math. Cong., Montreal (1961), 109-172.
[2] C. Ehresmann, S. Weishu, Sur les espaces feuilletés: théorème de stabilité, C.R. Acad. Sci. Paris 243 (1956), 344-346.
[3] A. Piątkowski, On the prefoliation of a K-differential space, Bull. Soc. Sci. Lettr. de Łódź, 50 (2000), 11-22.
[4] J. Pradines, How to define the differential graph of a singular foliation, Cahiers Top. Geom. Diff. XXVI, 4 (1985), 339-380.
[5] R. Reeb, Sur certaines propriétés topologiques des variétés feuilletées, Act. Sci. et Indust. No 1183, Hermann Paris, 1952.
[6] R. Sikorski, Introduction to Differential Geometry (in Polish), PWN Warszawa, 1972.
[7] P. Stefan, Accessible sets, orbits and foliations with singularities, Proc. London Math. Soc. 29 (1974), 699-713.
[8] H. J. Sussmann, Orbits of families of vector fields and integrability of distributions, Trans. Amer. Math. Soc. 79 (1973), 171-188.
[9] P. Ver Eecke, Le groupoide fondamental d'un feuilletage de Stefan, Publicationes de Seminario Matemático Garcia de Galdeano, Serie II, Sec. 3, No 6, Universidad de Zaragoza, 1986.
[10] W. Waliszewski, Inducing and coinducing in general differential spaces, Demonstratio Math. 24 No 3-4 (1991), 657-664.
[11] W. Waliszewski, Lecture notes, (unpublished).
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