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

• Autorzy: Piątkowski A.
• 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

EN

differential space; vector fields; differential geometry

PL

przestrzeń różniczkowa; pole wektorowe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• 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

Bibliografia

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• [3] A. Piątkowski, On the prefoliation of a K-differential space, Bull. Soc. Sci. Lettr. de Łódź, 50 (2000), 11-22.
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• [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• [11] W. Waliszewski, Lecture notes, (unpublished).