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Section
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Mathematics
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Title
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Conformal connection with scalar curvature
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Author(-s)
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Krivonosov L.N.a,
Luk'yanov V.A.a
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Affiliations
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Nizhni Novgorod State Technical Universitya
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Abstract
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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.
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Keywords
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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
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UDC
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514.756.2
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MSC
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53A30
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DOI
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10.20537/vm180103
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Received
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12 November 2017
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Language
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Russian
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Citation
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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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References
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- Krivonosov L.N., Luk'yanov V.A. The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space, Siberian Journal of Pure and Applied Mathematics, 2017, issue 2, pp. 21-38 (in Russian).
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- Krivonosov L.N., Luk'yanov V.A. Gauge-invariant tensors of 4-manifold with conformal torsion-free connection and their applications for modeling of space-time, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2014, issue 2 (35), pp. 180-198 (in Russian). DOI: 10.14498/vsgtu1291
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Full text
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