| 1. | Trigonometry on surfaces of negative curvature is part of hyperbolic geometry.
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| 2. | If it were actually open, it would have negative curvature throughout.
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| 3. | Similar examples are CAT spaces of negative curvature.
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| 4. | In 1939 Hopf established ergodicity of the geodesic flow on manifolds of constant negative curvature.
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| 5. | The presence of two acyl chains but no headgroup results in a large negative curvature in membranes.
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| 6. | Here, the largest circle is taken as having negative curvature with respect to the other three.
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| 7. | Alternatively, the plane can also be given a metric which gives it constant negative curvature giving the hyperbolic plane.
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| 8. | His foundational work on geometry and symbolic dynamics continued in 1898 with the study of geodesics on surfaces of negative curvature.
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| 9. | Euclidean ) plane is a surface of constant zero curvature, and a hyperbolic plane is a surface of constant negative curvature.
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| 10. | One celebrated example of Anosov flow is given by the geodesic flow on a surface of constant negative curvature, cf Hadamard billiards.
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