## Duke Mathematical Journal

### Spherical rank rigidity and Blaschke manifolds

#### Abstract

In this paper we give a characterization of locally compact rank one symmetric spaces, which can be seen as an analogue of Ballmann's and Burns and Spatzier's characterizations of nonpositively curved symmetric spaces of higher rank, as well as of Hamenstädt's characterization of negatively curved symmetric spaces. Namely, we show that a complete Riemannian manifold $M$ is locally isometric to a compact, rank one symmetric space if $M$ has sectional curvature at most $1$ and each normal geodesic in $M$ has a conjugate point at $π$.

#### Article information

Source
Duke Math. J., Volume 128, Number 1 (2005), 65-81.

Dates
First available in Project Euclid: 17 May 2005

https://projecteuclid.org/euclid.dmj/1116361227

Digital Object Identifier
doi:10.1215/S0012-7094-04-12813-1

Mathematical Reviews number (MathSciNet)
MR2137949

Zentralblatt MATH identifier
1082.53051

#### Citation

Shankar, K.; Spatzier, R.; Wilking, B. Spherical rank rigidity and Blaschke manifolds. Duke Math. J. 128 (2005), no. 1, 65--81. doi:10.1215/S0012-7094-04-12813-1. https://projecteuclid.org/euclid.dmj/1116361227

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