Kruglov V. Parabolic and saddle foliations and distributions on 3-manifolds.

Українська версія

Thesis for the degree of Candidate of Sciences (CSc)

State registration number

0410U001210

Applicant for

Specialization

  • 01.01.04 - Геометрія і топологія

11-01-2010

Specialized Academic Board

Д 64.175.01

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine

Essay

Dissertation studies contact structures and foliations on closed 3-manifolds. The main goal is the study of interactions between geometric and topological properties of contact structures and foliations. Methods of study include the following: Riemannian geometry, geometric topology, Bochner technique. The following main results were proved in the dissertation: uniformization of contact structures on 3-manifolds, it was proved that every closed orientable 3-manifold admits a saddle and parabolic foliations, it was shown that every contact structure with vanishing Euler class on a closed 3-manifold is saddle, it was shown that every contact structure on a closed orientable 3-manifold is parabolic, existence theorem for totally geodesic contact structures on closed quotients of Thurston model geometries was proved.

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