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Riemannian structures on higher order frame bundles over Riemannian manifolds. (English) Zbl 1132.58003

Summary: We describe all \({\mathcal M} f_m\)-natural operators \(A : {\mathcal R}iem \to {\mathcal R}iem\,P^r\) transforming Riemannian structures \(g\) on \(m\)-dimensional manifolds \(M\) into Riemannian structures \(A(g)\) on the \(r\)-th order frame bundle \(P^rM = \text{inv}J_0^r(\mathbb R^m,M)\) over \(M\).

MSC:

58A20 Jets in global analysis
58A32 Natural bundles
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