## Ricci type identities for non-basic differentiation in Otsuki spaces.(English)Zbl 1053.53008

In $$N$$-dimensional Otsuki spaces the tensor field $$P^i_j$$ and two types of connection coefficients $${}'\Gamma$$ and $${}''\Gamma$$ have an important role. The basic covariant derivative for the tensor $$V^i_j$$ is defined by $V^i_{j;k}=V^i_{j,k}+{}'\Gamma_p{}^i{}_kV^p_j-{}''\Gamma_j{}^p{}_kV^i_p,$ and the nonbasic covariant derivative by $$V^i_{j\underset{1}\| k}=P^i_pP^q_jV^p_{q;k}$$. The other nonbasic covariant derivative $$\underset{2}\| k$$ is obtained from above if the index $$k$$ in $${}'\Gamma$$ and $${}''\Gamma$$ is on the first place; in $$\underset{3}\| k$$ and $$\underset{4}\| k$$ $$k$$ only on one place changes the place.
The author proves several theorems with Ricci-type identities by using different nonbasic covariant derivatives $$\underset\alpha\| k$$, $$\alpha=1,2,3,4$$.

### MSC:

 53A40 Other special differential geometries 53B05 Linear and affine connections
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