Every complete, connected, simply-connected manifold of constant negative curvature " 1 is isometric to the real hyperbolic space \ mathbb { H } ^ n.
22.
The image like an expanding horn on the right shows a universe with negative curvature in time, and no finite end, no boundary in the upward time dimension.
23.
When M is of negative curvature and \ varepsilon is smaller than the Margulis constant for \ widetilde M the structure of the components of the thin part is very simple.
24.
One species has a Type II functional response-which occurs when individuals must spend time handling handling resources before moving on to the next resource-and has negative curvature.
25.
In geometry, methods of ergodic theory have been used to study the geodesic flow on Riemannian manifolds, starting with the results of Eberhard Hopf for Riemann surfaces of negative curvature.
26.
In 1898 Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature, called " Hadamard's billiards ".
27.
Conversely, adding a diamond-shaped "'gusset "'produces negative curvature at its tips and positive curvature at its middle ( useful in designing stuffed animals ).
28.
He proposed that harmonic maps be used to prove rigidity of the complex structure for K�hler manifolds with strongly negative curvature, a program that was successfully carried out by Yum-Tong Siu.
29.
General relativity merely adds a connection between the spatial curvature of the universe and the energy of such a particle : positive total energy implies negative curvature and negative total energy implies positive curvature.
30.
Showed that a complete immersed surface in "'R "'3 cannot have constant negative curvature, and show that the curvature cannot be bounded above by a negative constant.
