Nonpositive curvature foliations on 3-manifolds with bounded total absolute curvature of leaves

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.

Keywords

• Foliations
• B-foliations
• non-negative curvature
• 3-dimensional manifolds
• Cohn-Vossen theorem