Complete Projective Foliations with Zero Transverse Curvature

Student: Yunusova Rozaliya

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

Educational Programme: Mathematics (Bachelor)

Final Grade: 8

Year of Graduation: 2021

As is known, any foliation (M, F) on a compact manifold M has a minimal set. Generally speaking, this is not true for foliations on non-compact manifolds. Beniere and Meigniez, Inaba and others have constructed examples of foliations without minimal sets on non-compact manifolds. In this work, we prove the existence of a minimal set for any complete projective foliation with zero transversal curvature without assuming the compactness of the foliated manifold. In this work, we also construct a continuum family of projective foliations on closed 3-manifolds and investigate the structure of these foliations and their minimal sets.

Full text (added May 29, 2021)

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