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It has been suggested that this article be merged with Bochner identity. (Discuss) Proposed since October 2007.

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In mathematics, Bochner's formula : <math> \triangle f = |\nabla X|^2 - Ric(X,X) <\math>, where <math> f = \frac{1}{2}g(X,X) <\math>, is a significant result of Salomon Bochner in differential geometry. Loosely speaking, it says that the difference between the two Laplacian-like operators on the tangent bundle of a Riemannian manifold is a zero-order operator determined by the Ricci curvature. It is an example of a Weitzenböck identity. Bochner used this formula to prove the Bochner vanishing theorem.

The Bochner formula is often proved using supersymmetry or Clifford algebra methods.

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