Description

• Title:
  Module of geodesic foliation on the flat torus
• Creator:
  Kaźmierczak, Anna
• Contributor:
  Faculty of Mathematics and Computer Science University of Lodz, Poland;
  akaz@math.uni.lodz.pl
• Description:
  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.
• Object availability:
  free access
• Rights: http://creativecommons.org/licenses/by-nc-nd/4.0 ;
  Attribution-NonCommercial-NoDerivatives 4.0 Międzynarodowe
• Date:
  2021.11.15;
  2014
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Politechniki Częstochowskiej
• Relation:
  Journal of Applied Mathematics and Computational Mechanics;13;
  4
• Subject:
  flat torus;
  module of a family of submanifolds;
  foliation;
  geodesics
• Identifier:
  Kaźmierczak, 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.2014.4.08;
  2299-9965;
  http://hdl.handle.net/11089/39762 ;
  2353-0588;
  10.17512/jamcm.2014.4.08
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  seek permission
• Type:
  image