Geometry of Complete Affine Foliations

Student: Galdina Elizaveta

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Mathematics (Bachelor)

Final Grade: 7

Year of Graduation: 2019

The aim of this paper is to study the structure of complete affine foliations of arbitrary codimension q on n-dimensional manifolds, where 0 < q < n. In this case, the compactness of the layered varieties is not assumed. The main result of the work is the reduction of the problem of existence of closed layers, everywhere dense layers and minimal sets for the specified class of foliations to the corresponding problems for global holonomy groups representing some countable subgroups of the affine group Aff(Aq) q-dimensional affine space Aq.

Full text (added May 15, 2019)

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