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Ricci Form

The Ricci form of a Kähler manifold is the real closed form of type (1,1) obtained from the Ricci tensor R and the complex structure J by

rho(X,Y)=R(JX,Y).

In local holomorphic coordinates, if g_(jk^_) is the Kähler metric, then

rho=-ipartialpartial^_lndet(g_(jk^_)).

Its cohomology class is 2pi times the first Chern class of the manifold.

See also

Calabi Conjecture, Chern Class, Kähler Form, Ricci Curvature Tensor

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References

Griffiths, P. and Harris, J. Principles of Algebraic Geometry. New York: Wiley, 1978.

Cite this as:

Weisstein, Eric W. "Ricci Form." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RicciForm.html

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