RIEMANNIAN METRICS WITH THE PRESCRIBED CURVATURE TENSOR AND ALL ITS COVARIANT DERIVATIVES AT ONE-POINT

On an n-dimensional vector space. equipped with a scalar product, we p rescribe (0, 4)-, (0, 5)-, ... type tensors R(0), R (1), ..., satisfyi ng the well-known conditions for a curvature tensor and its derivative s and furthermore certain inequalities for the absolute values of the components of R(k). Then there is an analytic Riemannian metric g on a n open ball of the Cartesian space R(n)[u1, ..., u(n)] for which u1, . .., u(n) are normal coordinates and (del(k)R)0 = R(k) (k = 0, 1, 2, .. .) hold under an identification of the tangent space T0R(n) at the ori gin with the vector space; del(k)R denote the curvature tensor and its covariant derivatives with respect to the Levi-Civita connection del of g, respectively