This article is cited in 11 papers

The topology of group extensions of C systems

M. I. Brin

National Institute for Economic Investigations, USSR

Abstract: The paper is concerned with the topological and metric properties of group extensions of C systems. The basic theorem describes the topologically transitive component, the ergodic component, and the K component of a group extension of a C system. It is shown that each of these components is a group sub-bundle of a principal bundle in which the group extension acts. The frame flow on a manifold of negative curvature is seen to be a special case of a group of extension of a C system. It is shown that the space of frames on a compact three-dimensional manifold with negative curvature does not have any group sub-bundles, so that the frame flow on manifolds of this class is topologically transitive, ergodic, and a K system.

UDC: 513.838

Received: 05.03.1975

 English version: Mathematical Notes, 1975, 18:3, 858–864

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