The Gaussian curvature coincides with the sectional curvature of the surface.
2.
Let K _ g represent the sectional curvature.
3.
The sectional curvature is, and any point of can serve as a soul of.
4.
Here the sectional curvature is positive everywhere.
5.
The rank is always at least one, with equality if the sectional curvature is positive or negative.
6.
The Ricci curvature is determined by the sectional curvatures of a Riemannian manifold, but generally contains less information.
7.
The holomorphic sectional curvature is closely tied to the properties of " X " as a complex manifold.
8.
Generalising the example of closed surfaces, the fundamental groups of compact Riemannian manifolds with strictly negative sectional curvature are hyperbolic.
9.
The hyperbolic plane ( and more generally any Hadamard manifolds of sectional curvature \ le-1 ) is 2-hyperbolic.
10.
This K�hler metric has nonpositive bisectional curvature, negative holomorphic sectional curvature, and Ricci curvature, both with negative upper bound.
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