# Totally geodesic hypersurfaces in manifolds of nonpositive curvature

Goette, S; Schroeder, Viktor (1995). Totally geodesic hypersurfaces in manifolds of nonpositive curvature. Manuscripta Mathematica, 86(2):169-184.

## Abstract

In this paper we determine the structure of an embedded totally geodesic hypersurface F or, more generally, of a totally geodesic hypersurface F without selfintersections under arbitrarily small angles in a compact manifold M of nonpositive sectional curvature. Roughly speaking, in the case of locally irreducible M the result says that F has only finitely many ends, and each end splits isometrically as K ⨯ (0, ∞), where K is compact.

## Abstract

In this paper we determine the structure of an embedded totally geodesic hypersurface F or, more generally, of a totally geodesic hypersurface F without selfintersections under arbitrarily small angles in a compact manifold M of nonpositive sectional curvature. Roughly speaking, in the case of locally irreducible M the result says that F has only finitely many ends, and each end splits isometrically as K ⨯ (0, ∞), where K is compact.

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