Geodesic
On scalar and total scalar curvatures of Riemann-Cartan manifolds
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 291

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The concept of the Riemann-Cartan manifold was introduced by E.~Cartan. The Riemann-Cartan manifold is a triple $(M,g,\bar\nabla)$, where $(M,g)$ is a Riemann $n$-dimensional $(n\geq2)$ manifold with linear connection $\bar\nabla$ having nonzero torsion $\bar S$ such that $\bar\nabla g=0$. In our paper, we have considered scalar and total scalar curvatures of the Riemann-Cartan manifold $(M,g,\bar\nabla)$ and proved some formulas connecting these curvatures with scalar and total scalar curvatures of the Riemannian $(M,g)$. In particular we have analyzed these formulas for the case of Weitzenbök manifolds. And in an inference we have proved some vanishing theorems.
Classification : 53C05 53C20
Keywords: Riemann-Cartan manifold, Scalar and complete scalar curvature, Vanishing theorems 
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     title = {On scalar and total scalar curvatures of {Riemann-Cartan} manifolds},
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Sergey Stepanov; Irina Tsyganok; Josef Mikeš. On scalar and total scalar curvatures of Riemann-Cartan manifolds. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 2, p. 291 . http://geodesic.mathdoc.fr/item/KJM_2011_35_2_a7/