Pinching constant

This article defines a scalar value (viz, a real number) associated with a Riemannian manifold. This real number depends both on the underlying differential manifold and the Riemannian metric

Definition

The pinching constant for a Riemannian metric on a (compact) differential manifold is defined as the ratio $\mathrm{\Delta }/\delta$ where $\mathrm{\Delta }$ and $\delta$ are, respectively, the maximum and minimum values taken by sectional curvatures for tangent planes on the manifold.