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Russia Nizhni Novgorod
Section Mathematics
Title Conformal connection with scalar curvature
Author(-s) Krivonosov L.N.a, Luk'yanov V.A.a
Affiliations Nizhni Novgorod State Technical Universitya
Abstract 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, connection matrix, curvature matrix of connection, gauge transformations, rescalable scalar, conformal connection with scalar curvature, partition of unity, gauge-invariant metric
UDC 514.756.2
MSC 53A30
DOI 10.20537/vm180103
Received 12 November 2017
Language Russian
Citation Krivonosov L.N., Luk'yanov V.A. Conformal connection with scalar curvature, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, vol. 28, issue 1, pp. 22-35.
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