Duke Mathematical Journal

Spherical rank rigidity and Blaschke manifolds

K. Shankar, R. Spatzier, and B. Wilking

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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

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

First available in Project Euclid: 17 May 2005

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]


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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