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
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.
Einstein equations, Yang–Mills equations, Hodge operator, Maxwell's equations, manifold of conformal connection with torsion and without torsion.
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Received in revised form: 29.01.2012
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
\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.
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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
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
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
L. N. Krivonosov, V. A. Lukyanov, “Konformnaya svyaznost so skalyarnoi kriviznoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 22–35
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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