High Quality Content by WIKIPEDIA articles! In mathematics, in particular in differential geometry, mathematical physics, and representation theory a Weitzenbock identity expresses a relationship between two second-order elliptic operators on a manifold with the same leading symbol. Usually Weitzenbock formulae are implemented for G-invariant self-adjoint operators between vector bundles associated to some principal G-bundle, although the precise conditions under which such a formula exists are difficult to formulate. Instead of attempting to be completely general, then, this article presents three examples of Weitzenbock identities: from Riemannian geometry, spin geometry, and complex analysis. In mathematics — specifically, differential geometry — the Bochner identity is an identity concerning harmonic maps between Riemannian manifolds. The identity is named after the American mathematician Salomon Bochner.

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