## 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

### Keywords:

pseudotensors; Otsuki spaces; covariant derivative
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