Pinching constant

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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 \Delta/\delta where \Delta and \delta are, respectively, the maximum and minimum values taken by sectional curvatures for tangent planes on the manifold.