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Journal of Siberian Federal University. Mathematics & Physics, 2012, Volume 5, Issue 3, Pages 393–408 (Mi jsfu256)  

This article is cited in 6 scientific papers (total in 6 papers)

Einstein's equations on a $4$-manifold of conformal torsion-free connection

Leonid N. Krivonosova, Vyacheslav A. Luk'yanovb

a Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
b Nizhny Novgorod State Technical University, Nizhny Novgorod reg., Zavolzh'e, Russia
Full-text PDF (237 kB) Citations (6)
References:
Abstract: The main defect of Einstein equations – non geometrical right part – is eliminated. The key concept of equidual tensor is introduced. It appeared to be in a close relation both with Einstein's equations, and with Yang–Mills equations. The criterion of equidual basic affinor of conformal connection manifold without torsion is received. Decomposition of the basic affinor into a sum of equidual, conformally invariant and irreducible summands is found. A. Z. Petrov's algebraic classification is generalized. Einstein equations are given a new variational foundation and their geometrical nature is found. Geometric sense of acceleration and dilatation gauge transformations is specified.
Keywords: Einstein equations, Yang–Mills equations, Hodge operator, Maxwell's equations, manifold of conformal connection with torsion and without torsion.
Received: 25.09.2011
Received in revised form: 29.01.2012
Accepted: 29.03.2012
Document Type: Article
UDC: 512.54
Language: Russian
Citation: Leonid N. Krivonosov, Vyacheslav A. Luk'yanov, “Einstein's equations on a $4$-manifold of conformal torsion-free connection”, J. Sib. Fed. Univ. Math. Phys., 5:3 (2012), 393–408
Citation in format AMSBIB
\Bibitem{KriLuk12}
\by Leonid~N.~Krivonosov, Vyacheslav~A.~Luk'yanov
\paper Einstein's equations on a~$4$-manifold of conformal torsion-free connection
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2012
\vol 5
\issue 3
\pages 393--408
\mathnet{http://mi.mathnet.ru/jsfu256}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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