Weitzenböck Identity
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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…mehr

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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.