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