Main Page | See live article | Alphabetical index In mathematics, the scalar curvature of a surface is the familiar Gaussian curvature. For higher-dimensional manifolds, it is double of the sum of all the sectional curvatures along all the 2-planes spanned by some orthonormal frame. It is also the full trace of the Ricci curvature as well as of the curvature tensor. This article is from Wikipedia. All text is available under the terms of the GNU Free Documentation License.