Geodesic
Conformal connection with scalar curvature
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 22-35 Cet article a éte moissonné depuis la source Math-Net.Ru

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A conformal connection with scalar curvature is defined as a generalization of a pseudo-Riemannian space of constant curvature. The curvature matrix of such connection is computed. It is proved that on a conformally connected manifold with scalar curvature there is a conformal connection with zero curvature matrix. We give a definition of a rescalable scalar and prove the existence of rescalable scalars on any manifold with conformal connection where a partition of unity exists. It is proved: 1) on any manifold with conformal connection and zero curvature matrix there exists a conformal connection with positive, negative and alternating scalar curvature; 2) on any conformally connected manifold there exists a global gauge-invariant metric; 3) on a hypersurface of a conformal space the induced conformal connection can not be of nonzero scalar curvature.
Keywords: manifold with conformal connection, curvature matrix of connection, gauge transformations, conformal connection with scalar curvature, partition of unity, gauge-invariant metric.
Mots-clés : connection matrix, rescalable scalar 
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L. N. Krivonosov; V. A. Luk'yanov. Conformal connection with scalar curvature. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 28 (2018) no. 1, pp. 22-35. http://geodesic.mathdoc.fr/item/VUU_2018_28_1_a2/

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