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Totally geodesic hypersurfaces in manifolds of nonpositive curvature


Goette, S; Schroeder, V (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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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:1995
Deposited On:29 Nov 2010 16:28
Last Modified:05 Apr 2016 13:27
Publisher:Springer
ISSN:0025-2611
Free access at:Related URL. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/BF02567986
Related URLs:http://www.digizeitschriften.de/dms/img/?PPN=PPN365956996_0086&DMDID=dmdlog16
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0830.53034
http://www.ams.org/mathscinet-getitem?mr=1317742

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