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A rigidity theorem for simply connected manifolds without conjugate points

Published online by Cambridge University Press:  01 August 1998

CHRISTOPHER B. CROKE  and
BRUCE KLEINER
CHRISTOPHER B. CROKE
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6317, USA
BRUCE KLEINER
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA
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Abstract

In this paper we show that manifolds without conjugate points exhibit rigidity phenomena similar to that studied in [BGS, Section I.5]. The main theorem is that if $X$ is a complete, simply connected Riemannian manifold without conjugate points, and $M=X\times R$ is given the Riemannian product metric $g$, then any metric without conjugate points on $M$ which agrees with $g$ outside a compact set is isometric to $g$.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 4 , August 1998 , pp. 807 - 812
Copyright
© 1998 Cambridge University Press

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