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This article is cited in 5 scientific papers (total in 5 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
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.Ż. 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.
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UDC:
512.54 Received: 25.09.2011 Received in revised form: 29.01.2012 Accepted: 29.03.2012
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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http://mi.mathnet.ru/eng/jsfu256 http://mi.mathnet.ru/eng/jsfu/v5/i3/p393
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This publication is cited in the following articles:
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L. N. Krivonosov, V. A. Lukyanov, “Kalibrovochno-invariantnye tenzory 4-mnogoobraziya konformnoi svyaznosti bez krucheniya”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 2(35) (2014), 180–198
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V. A. Lukyanov, L. N. Krivonosov, “Uravneniya Yanga-Millsa na 4-mnogoobraziyakh konformnoi svyaznosti bez krucheniya s razlichnymi signaturami”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 21:4 (2017), 633–650
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L. N. Krivonosov, V. A. Luk'yanov, “The structure of the main tensor of conformally connected torsion-free space. Conformal connections on hypersurfaces of projective space”, J. Math. Sci., 231:2 (2018), 189–205
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L. N. Krivonosov, V. A. Lukyanov, “Konformnaya svyaznost so skalyarnoi kriviznoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 22–35
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L. N. Krivonosov, V. A. Lukyanov, “Osnovnaya teorema dlya (anti)avtodualnoi konformnoi svyaznosti bez krucheniya na chetyrekhmernom mnogoobrazii”, Izv. vuzov. Matem., 2019, no. 2, 29–38
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