Does Anosov geodesic flow imply asphericity?When is an Anosov diffeomorphism mixing?When is the time evolution of a Hamiltonian system described by the geodesic flow on a Riemannian manifold?What are the zero entropy invariant measures for an Anosov geodesic flow?Geodesics and harmonic map heat flowDoes null geodesic flow live on a natural compact bundle?Simply connected manifolds with dense geodesics on the tangent bundleFinding a 1-form adapted to a smooth flowHolder potentials over time-one map of Anosov flowErgodicity of a measure preserving Anosov flowA kind of converse to the Hopf theorem on ergodicity of geodesic flow in negative curvature
Does Anosov geodesic flow imply asphericity?
When is an Anosov diffeomorphism mixing?When is the time evolution of a Hamiltonian system described by the geodesic flow on a Riemannian manifold?What are the zero entropy invariant measures for an Anosov geodesic flow?Geodesics and harmonic map heat flowDoes null geodesic flow live on a natural compact bundle?Simply connected manifolds with dense geodesics on the tangent bundleFinding a 1-form adapted to a smooth flowHolder potentials over time-one map of Anosov flowErgodicity of a measure preserving Anosov flowA kind of converse to the Hopf theorem on ergodicity of geodesic flow in negative curvature
$begingroup$
Let $(M, g)$ be a closed smooth Riemannian manifolds with Anosov geodesic flow, does it implies that $M$ is an aspherical manifold?
I am thinking it is not known yet?
dg.differential-geometry riemannian-geometry ds.dynamical-systems
edited 7 hours ago
YCor
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$begingroup$
Let $(M, g)$ be a closed smooth Riemannian manifolds with Anosov geodesic flow, does it implies that $M$ is an aspherical manifold?
I am thinking it is not known yet?
dg.differential-geometry riemannian-geometry ds.dynamical-systems
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
$endgroup$
add a comment |
$begingroup$
Let $(M, g)$ be a closed smooth Riemannian manifolds with Anosov geodesic flow, does it implies that $M$ is an aspherical manifold?
I am thinking it is not known yet?
dg.differential-geometry riemannian-geometry ds.dynamical-systems
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
$endgroup$
Let $(M, g)$ be a closed smooth Riemannian manifolds with Anosov geodesic flow, does it implies that $M$ is an aspherical manifold?
I am thinking it is not known yet?
dg.differential-geometry riemannian-geometry ds.dynamical-systems
dg.differential-geometry riemannian-geometry ds.dynamical-systems
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
edited 7 hours ago
YCor
30k4 gold badges89 silver badges144 bronze badges
30k4 gold badges89 silver badges144 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
asked 8 hours ago
user60933user60933
3261 silver badge8 bronze badges
asked 8 hours ago
user60933user60933
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3261 silver badge8 bronze badges
add a comment |
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1 Answer
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W. Klingenberg in [Riemannian Manifolds With Geodesic Flow of Anosov Type, Annals of Mathematics, Vol. 99, No. 1, 1974, pp. 1-13] proved among other things that a closed Riemannian manifold with Anosov geodesic flow does not have conjugate points, and hence the exponential map at any point is a covering map. In particular, the manifold is aspherical.
answered 6 hours ago
Igor BelegradekIgor Belegradek
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1 Answer
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1 Answer
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$begingroup$
W. Klingenberg in [Riemannian Manifolds With Geodesic Flow of Anosov Type, Annals of Mathematics, Vol. 99, No. 1, 1974, pp. 1-13] proved among other things that a closed Riemannian manifold with Anosov geodesic flow does not have conjugate points, and hence the exponential map at any point is a covering map. In particular, the manifold is aspherical.
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
$endgroup$
add a comment |
$begingroup$
W. Klingenberg in [Riemannian Manifolds With Geodesic Flow of Anosov Type, Annals of Mathematics, Vol. 99, No. 1, 1974, pp. 1-13] proved among other things that a closed Riemannian manifold with Anosov geodesic flow does not have conjugate points, and hence the exponential map at any point is a covering map. In particular, the manifold is aspherical.
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
$endgroup$
add a comment |
$begingroup$
W. Klingenberg in [Riemannian Manifolds With Geodesic Flow of Anosov Type, Annals of Mathematics, Vol. 99, No. 1, 1974, pp. 1-13] proved among other things that a closed Riemannian manifold with Anosov geodesic flow does not have conjugate points, and hence the exponential map at any point is a covering map. In particular, the manifold is aspherical.
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
$endgroup$
W. Klingenberg in [Riemannian Manifolds With Geodesic Flow of Anosov Type, Annals of Mathematics, Vol. 99, No. 1, 1974, pp. 1-13] proved among other things that a closed Riemannian manifold with Anosov geodesic flow does not have conjugate points, and hence the exponential map at any point is a covering map. In particular, the manifold is aspherical.
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
answered 6 hours ago
Igor BelegradekIgor Belegradek
19.7k1 gold badge44 silver badges127 bronze badges
19.7k1 gold badge44 silver badges127 bronze badges
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