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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 1, Pages 22–35
(Mi vuu617)
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MATHEMATICS
Conformal connection with scalar curvature
L. N. Krivonosov, V. A. Luk'yanov Nizhni Novgorod State Technical University, ul. Minina, 24, Nizhni Novgorod, 603950, Russia
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.
DOI:
https://doi.org/10.20537/vm180103
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Bibliographic databases:
UDC:
514.756.2
MSC: 53A30 Received: 12.11.2017
Citation:
L. N. Krivonosov, V. A. Luk'yanov, “Conformal connection with scalar curvature”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 22–35
Citation in format AMSBIB
\Bibitem{KriLuk18}
\by L.~N.~Krivonosov, V.~A.~Luk'yanov
\paper Conformal connection with scalar curvature
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 22--35
\mathnet{http://mi.mathnet.ru/vuu617}
\crossref{https://doi.org/10.20537/vm180103}
\elib{https://elibrary.ru/item.asp?id=32697213}
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