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Induced mappings of the Riemannian spaces of the second-order approximation. (Russian. English summary) Zbl 1316.53018

Summary: For a nontrivial geodesic mapping \(\gamma\) of the Riemannian spaces \(\overline V_n\) and \(V_n\), we construct the spaces of the second-order approximation \(\widetilde{\overline V}^2_n\) and \(\widetilde V^2_n\). We study the mapping \(\widetilde\gamma\), which is induced by the mapping \(\gamma\). Also we obtain the deformation tensor of the mapping \(\widetilde\gamma\) in an explicit form.

MSC:

53B20 Local Riemannian geometry