# Pinching constant

From Diffgeom

*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 where and are, respectively, the maximum and minimum values taken by sectional curvatures for tangent planes on the manifold.