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Ricci type identities for basic differentiation and curvature tensors in Otsuki spaces. (English) Zbl 1025.53005

In Otsuki spaces the covariant derivative is defined by \[ V^{i1}_{j|k} =\partial_kV^i_j+{}'\Gamma^i_{pk}V^p_j-{}''\Gamma^{ p }_{j k}V^i_p. \] \(V^{i2}_{j|k}\) is obtained from \(V^{i1}_{j|k}\) if the index \(k\) changes the place with \(p\) and \(j\) in \('\Gamma\) and \(''\Gamma\) respectively. \(V^{i3}_{j|k}\) (\(V^{i4}_{j|k}\)) is obtained from \(V^{i1}_{j|k}\) if \(p\) and \(k\) change the place in \('\Gamma\) (the indices \(k\) and \(j\) change the place in \(''\Gamma\)).
By using these different types of basic covariant derivatives several Ricci type identities are obtained.

MSC:

53B05 Linear and affine connections
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