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Totally geodesic hypersurfaces in manifolds of nonpositive curvature

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Abstract

In this paper we determine the structure of an embedded totally geodesic hypersurfaceF or, more generally, of a totally geodesic hypersurfaceF without selfintersections under arbitrarily small angles in a compact manifoldM of nonpositive sectional curvature. Roughly speaking, in the case of locally irreducibleM the result says thatF has only finitely many ends, and each end splits isometrically asK×(0, ∞), whereK is compact.

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Authors and Affiliations

  1. Mathematisches Institut der Universität Freiburg, Hebelstr. 29, D-79104, Freiburg, Germany

    Sebastian Goette

  2. Mathematisches Institut der Universität Zürich, Winterthurer Str. 190, CH-8057, Zürich, Switzerland

    Viktor Schroeder

Authors
  1. Sebastian Goette
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  2. Viktor Schroeder
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This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.

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Goette, S., Schroeder, V. Totally geodesic hypersurfaces in manifolds of nonpositive curvature. Manuscripta Math 86, 169–184 (1995). https://doi.org/10.1007/BF02567986

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  • DOI: https://doi.org/10.1007/BF02567986

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