One quantity encoding this property is decomposed into scalar, semi-traceless, and traceless components by the Kulkarni-Nomizu product.
This property is the infinitesimal holonomy around a closed loop according to the Ambrose-Singer theorem. The asymptotic behavior of one quantity encoding this property is given by the big-O of the affine parameter to the negative fifth by the peeling theorem. One quantity encoding this property is decomposed into scalar, semi-traceless, and traceless components by the Kulkarni-Nomizu product. One half times the metric tensor times the scalar version of this quantity appears in one term of the (*) Einstein field equation. One quantity used to define it can be expressed entirely in terms of the Christoffel symbols and their first derivatives. The Weyl tensor, the Ricci tensor, and the Riemann tensor all describe this property, which is zero for Euclidean geometry and negative for hyperbolic geometry. For 10 points, name this quantity which produces gravity according to the theory of relativity, the deviation from flatness.
This property is the infinitesimal holonomy around a closed loop according to the Ambrose-Singer theorem.
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