ricederived

Ricederived is an adjective used in mathematics and theoretical physics to describe quantities, constructions, or invariants that are derived directly from Ricci curvature or from the Ricci flow. The term emphasizes the origin of the object in the Ricci tensor, as opposed to quantities derived from the full Riemann curvature tensor or from other geometric data.

In differential geometry, ricederived measures may include scalar functions formed by contracting the Ricci tensor or quantities defined by applying operators to the Ricci tensor. In physics and geometric analysis, invariants built from the Ricci tensor or its contractions may be described as ricederived, distinguishing them from invariants constructed from other curvature components. The term is not uniformly standardized across all subfields; some authors prefer the hyphenated form “Ricci-derived” or simply describe the object as being derived from the Ricci tensor.

Usage examples are typically contextual and highly dependent on the specific mathematical framework. The label tends to be most common in expository writing or when contrasting objects that depend on Ricci curvature with those tied to the full Riemann tensor or to other curvature notions.

See also: Ricci curvature, Ricci tensor, scalar curvature, Ricci flow, differential geometry, geometric analysis, curvature invariants.