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/