Ricci Curvature Tensor

The Ricci curvature tensor, also simply known as the Ricci tensor (Parker and Christensen 1994), is defined by


where R^lambda_(mulambdakappa) is the Riemann tensor.

Geometrically, the Ricci curvature is the mathematical object that controls the growth rate of the volume of metric balls in a manifold.

See also

Bishop's Inequality, Campbell's Theorem, Einstein Tensor, Milnor's Theorem, Riemann Tensor, Scalar Curvature

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Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. Gravitation. San Francisco: W. H. Freeman, 1973.Parker, L. and Christensen, S. M. "The Ricci, Einstein, and Weyl Tensors." §2.7.1 in MathTensor: A System for Doing Tensor Analysis by Computer. Reading, MA: Addison-Wesley, pp. 30-32, 1994.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, pp. 135 and 142, 1972.

Referenced on Wolfram|Alpha

Ricci Curvature Tensor

Cite this as:

Weisstein, Eric W. "Ricci Curvature Tensor." From MathWorld--A Wolfram Web Resource.

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