1. Nonpositive curvature foliations on 3-manifolds with bounded total absolute curvature of leaves
- Author
-
Dmytry Bolotov
- Subjects
Pure mathematics ,Mathematics::Dynamical Systems ,Applied Mathematics ,lcsh:Mathematics ,010102 general mathematics ,non-negative curvature ,3-dimensional manifolds ,Curvature ,lcsh:QA1-939 ,01 natural sciences ,Foliations ,010305 fluids & plasmas ,B-foliations ,Absolute (philosophy) ,Bounded function ,0103 physical sciences ,Geometry and Topology ,Mathematics::Differential Geometry ,Cohn-Vossen theorem ,0101 mathematics ,Mathematics::Symplectic Geometry ,Analysis ,Mathematics - Abstract
In this paper we introduce a new class of foliations on Rie-mannian 3-manifolds, called B-foliations, generalizing the class of foliations of non-negative curvature. The leaves of B-foliations have bounded total absolute curvature in the induced Riemannian metric. We describe several topological and geometric properties of B-foliations and the structure of closed oriented 3-dimensional manifolds admitting B-foliations with non-positive curvature of leaves.
- Published
- 2018