Module of a geodesic foliation on the flat torus

• Autorzy: Kaźmierczak A.
• Języki publikacji: EN

Abstrakty

EN

We study properties of geodesic foliations on the flat, n-dimensional torus. Using the isomorphism of the Hodge star, we obtain some facts concerning compact totally geodesic surfaces (which are the leaves of geodesic foliations). We compute the p-module of a geodesic foliation. On the basis of these results, we derive a kind of reciprocity formula for the product of modules of two orthogonal foliations. We relate this product with the number of intersections of their leaves. We also obtain a formula for a product of modules of a finite number of geodesic foliations.

Słowa kluczowe

EN

flat torus; module of a family of submanifolds; foliation; geodesics

PL

foliacja; geodezja

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 4
• Strony: 61--72
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Kaźmierczak A.

• Faculty of Mathematics and Computer Science University of Lodz, Poland

Bibliografia

• [1] Ciska M., Pierzchalski A., On the modulus of level sets of conjugate submersions, Differential Geometry and its Applications, to appear.
• [2] Federer H., Geometric Measure Theory, Springer-Verlag, Berlin-Heidelberg -New York 1969.
• [3] Skolem T.H, Diophantische Gleichungen, Verlag von Julius Springer, Berlin 1938.
• [4] Warner F.W., Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, Berlin 1983.
• [5] Candel A., Conlon L., Foliations I. American Mathematical Society, Providence Rhode Island 2000.
• [6] Pierzchalski A., The k-module of level sets of differential mappings, Scientific Communications of the Czechoslovakian-GDR-Polish School on Differential Geometry at Boszkowo (1978), Math. Inst. Polish Acad. Sci., Warsaw, 180-185 1979.