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Riemannian Metrics with the Prescribed Curvature Tensor and all Its Covariant Derivatives at One Point by Oldřich Kowalski; Martin Belger is a Mathematics article available to read on EtoBox.

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## Abstract On an __n__‐dimensional vector space, equipped with a scalar product, we prescribe (0, 4) ‐, (0, 5)‐, ... type tensors __R__^(0)^, __R__^(1)^, ..., satisfying the well‐known conditions for a curvature tensor and its derivatives and furthermore certain inequalities for the absolute values of the components of __R__^(k)^. Then there is an analytic Riemannian metric g on an open ball of the Cartesian space R^__n__^[__u__^1^, ..., __u^n^__] for which __u__^1^, ..., __u^n^__ are normal coordinates and (▽^(k)^__R__)~0~ = __R__^(k)^ (__k__ = 0, 1, 2, ...) hold under an identification of the tangent space __T__~0~R^__n__^ at the origin with the vector space; ▽^(k)^__R__ denote the curvature tensor and its covariant derivatives with respect to the Levi‐Civita connection ▽ of g, respectively.

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Author

Oldřich Kowalski; Martin Belger

Publisher

John Wiley and Sons; Wiley (John Wiley & Sons); Wiley - V C H Verlag GmbbH & Co.; Wiley (ISSN 0025-584X)

Published

1994

Language

EN

Field

Mathematics (Physical Sciences)