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 
are the components of the inverse of the metric
tensor and 
are the components of the Ricci curvature tensor.
See also
Calabi Flow,
Curvature,
Einstein-Hilbert Functional,
Einstein
Tensor,
Gaussian Curvature,
Graphical
Scalar Curvature Equation,
Mean Curvature,
Metric Tensor,
Radius
of Curvature,
Ricci Curvature Tensor,
Riemann Tensor
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References
Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation.
San Francisco, CA: 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 Curvature
Cite this as:
Weisstein, Eric W. "Scalar Curvature."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ScalarCurvature.html
Subject classifications
