Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-29T01:41:45.608Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)