Scalar curvature

This article defines a notion of curvature for a differential manifold equipped with a Riemannian metric

This article defines a scalar function on a manifold, viz a function from the manifold to real numbers. The scalar function may be intrinsic or defined in terms of some other structure/functions

Definition

Definition part

The scalar curvature associated to $(M,g)$ is defined as the trace of the Ricci curvature tensor.