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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2018, Volume 28, Issue 1, Pages 22–35 (Mi vuu617)  

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

Full text: PDF file (275 kB)
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Document Type: Article
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{http://elibrary.ru/item.asp?id=32697213}


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