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A capital R with four indices, the full description of curvature.
Also known as: Riemann tensor, Curvature tensor, R with four indices
The Riemann tensor carries everything there is to say about the curvature of a space, and it is zero exactly when the space is flat. Its physical meaning is tidal force: it says how two nearby free-falling objects drift apart.
Denotes the Riemann curvature tensor, the complete local description of a manifold's curvature.
Contexts: Laboratory
Vanishes identically if and only if the space is flat, which is the precise test for curvature.
Contexts: Laboratory
Describes tidal effects physically: it governs the relative acceleration of neighbouring geodesics.
Contexts: Laboratory
An italic capital letter R carrying one raised and three lowered small index letters.