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On some relations between curvature and metric tensors in Riemannian spaces

Mikeš, JosefLaitochová, JitkaPokorná, Olga — 2000

Proceedings of the 19th Winter School "Geometry and Physics"

The paper generalizes results of and [Dokl. Akad. Nauk, Ross. Akad. Nauk 351, No. 3, 295-296 (1996; Zbl 0895.53038) and Sib. Mat. Zh. 39, No. 4, 1005-1012 (1998; Zbl 0913.53019)] on the existence and uniqueness of a Riemannian metric on a domain in n given prescribed values for some of the components of the Riemann curvature tensor and initial values of the metric and its partial derivatives. The authors establish the construction (existence and uniqueness) of a metric tensor g i j in a semigeodesic...

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