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A rigidity theorem for manifolds without conjugate points

Published online by Cambridge University Press:  01 August 1998

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

Abstract

In this paper we show that some nonsimply connected manifolds without conjugate points exhibit rigidity phenomena similar to that studied in [BGS, section I.5]. This is a companion paper to [Cr-Kl1] that deals with the simply connected case. In particular, we show that one cannot make a nontrivial, compactly supported, change to a complete flat metric without introducing conjugate points.

Type
Research Article
Copyright
© 1998 Cambridge University Press

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