- Kulkarni–Nomizu product
In the mathematical field of
differential geometry , the Kulkarni–Nomizu product is defined for two (0,2)-tensors and gives as a result a (0,4)-tensor. If h and k are (0,2)-tensors, then the product is defined via::hcirc k(X_1,X_2,X_3,X_4):=h(X_1,X_3)k(X_2,X_4)+h(X_2,X_4)k(X_1,X_3)-h(X_1,X_4)k(X_2,X_3)-h(X_2,X_3)k(X_1,X_4) where the "X""j" are tangent vectors.
It is most commonly used to express the contribution that the
Ricci curvature (or rather, theSchouten tensor ) and theWeyl tensor each makes to the curvature of aRiemannian manifold . This so-calledRicci decomposition is useful inconformal geometry .References
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