# Rigidity of an open solid torus [closed]

Assume that $M$ is a 3-dimensional complete open Riemannian manifold homeomorphic to a open solid torus. If $M$ has no conjugate point, then it has a constant sectional curvature.

Is it right? Thank you in advance.

(This question is arise when I consider the following : Conjugate points in ${\rm Sl}(2,\mathbb{R})$)

## closed as off-topic by Hee Kwon Lee, Chris Godsil, Stefan Kohl, Jan-Christoph Schlage-Puchta, Neil HoffmanMar 23 '17 at 16:12

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• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Chris Godsil, Stefan Kohl, Neil Hoffman
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• The product of a unit disk in the hyperbolic plane, by the circle gices you a solid torus but it does not have constant sectional curvature. Anyway this should be asked at MSE. – Mikhail Katz Mar 22 '17 at 9:29