The scalar curvature, also called the "curvature scalar" (e.g., Weinberg 1972, p. 135; Misner et al. 1973, p. 222) or "Ricci scalar," is given by
 |
where 
is the metric tensor and 
is the Ricci
curvature tensor.
Scalar Curvature
See also
Curvature, Einstein Tensor, Gaussian Curvature, Mean Curvature, Metric Tensor, Radius of Curvature, Ricci Curvature Tensor, Riemann TensorExplore with Wolfram|Alpha
References
Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco: W. H. Freeman, p. 222, 1973.Wald, R. M. General Relativity. Chicago, IL: University of Chicago Press, p. 40, 1984.Weinberg, S. Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. New York: Wiley, p. 135, 1972.Referenced on Wolfram|Alpha
Scalar CurvatureCite this as:
Weisstein, Eric W. "Scalar Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ScalarCurvature.html