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Module of a geodesic foliation on the flat torus

Kaźmierczak A.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 4

61--72

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.