:: The high pressure and temperature of the venusian atmosphere would cause the horizon to have negative curvature due to extreme optical refraction.
12.
Negative curvature means curved hyperbolically, like a saddle surface or the Gabriel's Horn surface, similar to that of a trumpet bell.
13.
Since the space of meromorphic 1-forms is a 1-dimensional vector space over the curvature, zero curvature, or negative curvature.
14.
Early notable results of Bowditch include clarifying the classic notion of geometric finiteness for higher-dimensional Kleinian groups in constant and variable negative curvature.
15.
Nathaniel Friedman writes, " The surfaces [ of Longhurst's sculptures ] generally have appealing sections with negative curvature ( saddle surfaces ).
16.
That's the definition of a hypersphere; a torus has positive curvature at some places along its surface, negative curvature at others.
17.
On the doughnut, the surface around the'doughnut hole'is deformed with negative curvature while the surface outside is deformed with positive curvature.
18.
As a result, the universal cover of any closed manifold M of constant negative curvature " 1 is \ mathbb { H } ^ n.
19.
Dispersing boundary plays the same role for billiards as negative curvature does for Bernoulli, having a positive Kolmogorov-Sinai entropy and an exponential decay of correlations.
20.
Regions of negative curvature ( " 2 f / " c 2 2 f / " c 2 = 0 ) which are called the spinodes.
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