Zero-scalar curvature metric

This article defines a property that makes sense for a Riemannian metric over a differential manifold

This is the property of the following curvature being everywhere zero: scalar curvature

Definition

Symbol-free definition

A Riemannian metric on a differential manifold is said to be a zero-scalar curvature metric if the scalar curvature corresponding to this Riemannian metric is zero at all points.

Relation with other properties

Stronger properties

• Flat metric
• Ricci-flat metric

Weaker properties

• Constant-scalar curvature metric