Show simple item record

dc.contributor.authorKaźmierczak, Anna
dc.identifier.citationKaźmierczak, A. (2014). Module of a geodesic foliation on the flat torus. Journal of Applied Mathematics and Computational Mechanics, 13(4), 61-72. doi:10.17512/jamcm.2014.4.08pl_PL
dc.description.abstractWe 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.pl_PL
dc.publisherWydawnictwo Politechniki Częstochowskiejpl_PL
dc.relation.ispartofseriesJournal of Applied Mathematics and Computational Mechanics;13
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe*
dc.subjectflat toruspl_PL
dc.subjectmodule of a family of submanifoldspl_PL
dc.titleModule of geodesic foliation on the flat toruspl_PL
dc.contributor.authorAffiliationFaculty of Mathematics and Computer Science University of Lodz, Polandpl_PL
dc.referencesCiska M., Pierzchalski A., On the modulus of level sets of conjugate submersions, Differential Geometry and its Applications, to appear.pl_PL
dc.referencesFederer H., Geometric Measure Theory, Springer-Verlag, Berlin-Heidelberg -New York 1969.pl_PL
dc.referencesSkolem T.H, Diophantische Gleichungen, Verlag von Julius Springer, Berlin 1938.pl_PL
dc.referencesWarner F.W., Foundations of Differentiable Manifolds and Lie Groups, Springer-Verlag, Berlin 1983.pl_PL
dc.referencesCandel A., Conlon L., Foliations I. American Mathematical Society, Providence Rhode Island 2000.pl_PL
dc.referencesPierzchalski 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.pl_PL

Files in this item


This item appears in the following Collection(s)

Show simple item record

Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe
Except where otherwise noted, this item's license is described as Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe