For example, they gave a proof of the integral Novikof conjecture for compact Riemannian manifolds with non-positive sectional curvature.
12.
For example, every Hermitian manifold " X " with holomorphic sectional curvature bounded above by a negative constant is Kobayashi hyperbolic.
13.
For this reason, the Fubini Study metric is often said to have " constant " holomorphic " sectional curvature " equal to 4.
14.
In particular the lower bound for the sectional curvature of N is at least as big as the lower bound for the sectional curvature of M.
15.
In particular the lower bound for the sectional curvature of N is at least as big as the lower bound for the sectional curvature of M.
16.
Here, curvature refers to the sectional curvature of a space ( more precisely a manifold ) and is a single number determining its local geometry.
17.
When the sectional curvature is bounded from above, a corollary to the Rauch comparison theorem yields an analogous statement, but with the reverse inequality.
18.
The sectional curvature is said to be constant if it has the same value at every point and for every two-dimensional tangent plane at that point.
19.
Note that the conclusion is false if the sectional curvatures are allowed to take values in the " closed " interval [ 1, 4 ].
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