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J. Sib. Fed. Univ. Math. Phys., 2012, Volume 5, Issue 3, Pages 393–408 (Mi jsfu256)  

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.

Full text: PDF file (237 kB)
References: PDF file   HTML file
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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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  mathnet  crossref  zmath  elib
    2. 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  mathnet  crossref  zmath  elib
    3. 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  mathnet  crossref  crossref
    4. L. N. Krivonosov, V. A. Lukyanov, “Konformnaya svyaznost so skalyarnoi kriviznoi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 28:1 (2018), 22–35  mathnet  crossref  elib
    5. 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  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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