Topological Significance
The sign of the Yamabe invariant of holds important topological information. For example, is positive if and only if admits a metric of positive scalar curvature. The significance of this fact is that much is known about the topology of manifolds with metrics of positive scalar curvature.
Read more about this topic: Yamabe Invariant
Famous quotes containing the word significance:
“To grasp the full significance of life is the actor’s duty, to interpret it is his problem, and to express it his dedication.”
—Marlon Brando (b. 1924)