Assertion: differentiable manifold | /r/HasAspect | positive ricci curvature
Facets:
value: everywhere
type: LOCATION
Source sentences:
text: In some cases Hamilton was able to show that this works; for example, his original breakthrough was to show that if the Riemannian manifold has positive Ricci curvature everywhere, then the above procedure can only be followed for a bounded interval of parameter values, t ∈ [ 0 , T ) {\displaystyle t\in [0,T)} with T < ∞ {\displaystyle T<\infty } , and more significantly, that there are numbers c t {\displaystyle c_{t}} such that as t ↗ T {\displaystyle