Geodesic
Vanishing theorems for some classes of Riemann--Cartan manifolds
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 7-12

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In this paper, a classification of Riemann–Cartan manifolds based on the orthogonal decomposition of the torsion tensor is given. Problems on the existence of two classes $\wp_1\oplus\wp_2$ and $\wp_3$ of Riemann–Cartan spaces are discussed. 
@article{FPM_2010_16_2_a1,
     author = {I. A. Gordeeva},
     title = {Vanishing theorems for some classes of {Riemann--Cartan} manifolds},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {7--12},
     publisher = {mathdoc},
     volume = {16},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a1/}
}
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I. A. Gordeeva. Vanishing theorems for some classes of Riemann--Cartan manifolds. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 2, pp. 7-12. http://geodesic.mathdoc.fr/item/FPM_2010_16_2_a1/