Lichnerowicz Formula

 D^*Dpsi=del ^*del psi+1/4Rpsi-1/2F_L^+(psi),

where D is the Dirac operator D:Gamma(W^+)->Gamma(W^-), del is the covariant derivative on spinors, R is the scalar curvature, and F_L^+ is the self-dual part of the curvature of L.

See also

Lichnerowicz-Weitzenbock Formula

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Donaldson, S. K. "The Seiberg-Witten Equations and 4-Manifold Topology." Bull. Amer. Math. Soc. 33, 45-70, 1996.

Referenced on Wolfram|Alpha

Lichnerowicz Formula

Cite this as:

Weisstein, Eric W. "Lichnerowicz Formula." From MathWorld--A Wolfram Web Resource.

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