Automorphisms of Spacetime Manifold with Torsion

Vladimir Ivanovich Pan’Zhenskii; Olga Petrovna Surina

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2016)

  • Volume: 55, Issue: 1, page 87-94
  • ISSN: 0231-9721

Abstract

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In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann–Cartan 4-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to 7. In addition, in the case of the Riemann–Cartan n -dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to n ( n - 1 ) / 2 + 1 for any n > 2 .

How to cite

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Pan’Zhenskii, Vladimir Ivanovich, and Surina, Olga Petrovna. "Automorphisms of Spacetime Manifold with Torsion." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 55.1 (2016): 87-94. <http://eudml.org/doc/286694>.

@article{Pan2016,
abstract = {In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann–Cartan 4-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to 7. In addition, in the case of the Riemann–Cartan $n$-dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to $n(n-1)/2+1$ for any $n>2$.},
author = {Pan’Zhenskii, Vladimir Ivanovich, Surina, Olga Petrovna},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {Riemann–Cartan manifolds; automorphisms; semi-symmetric connection},
language = {eng},
number = {1},
pages = {87-94},
publisher = {Palacký University Olomouc},
title = {Automorphisms of Spacetime Manifold with Torsion},
url = {http://eudml.org/doc/286694},
volume = {55},
year = {2016},
}

TY - JOUR
AU - Pan’Zhenskii, Vladimir Ivanovich
AU - Surina, Olga Petrovna
TI - Automorphisms of Spacetime Manifold with Torsion
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2016
PB - Palacký University Olomouc
VL - 55
IS - 1
SP - 87
EP - 94
AB - In this paper we prove that the maximum dimension of the Lie group of automorphisms of the Riemann–Cartan 4-dimensional manifold does not exceed 8, and if the Cartan connection is skew-symmetric or semisymmetric, the maximum dimension is equal to 7. In addition, in the case of the Riemann–Cartan $n$-dimensional manifolds with semisymmetric connection the maximum dimension of the Lie group of automorphisms is equal to $n(n-1)/2+1$ for any $n>2$.
LA - eng
KW - Riemann–Cartan manifolds; automorphisms; semi-symmetric connection
UR - http://eudml.org/doc/286694
ER -

References

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  1. Gordeeva, I. A., Pan’zhenskii, V. I., Stepanov, S. E., Riemann–Cartan manifolds, . In: Modern Mathematics and Its Applications 123 Geometry, VINITI, Moscow, 2009, 110–141, (in Russian). (2009) MR2866744
  2. Tamm, I. E., On the curved momentum space, . In: Selected Papers 4, Springer-Verlag, Berlin, Heidelberg, 1991, 197–210; Selected Scientific Papers 2, Nauka, Moscow, 1975, 218–225. (1991) 
  3. Tamm, I. E., Vologodskii, V. G., On the use of curved momentum space in the construction of nonlocal Euclidean field theory, . In: Collection of Scientific Papers 2, Nauka, Moscow, 1975, 226–253, (in Russian). Princeton Univ. Press, Princetton, NJ, 1953; Inostrannaya Literatura, Moscow, 1957. (1953) 
  4. Pan’zhenskii, V. I., Maximally movable Riemannian spaces with torsion, . Math. Notes 85, 5-6 (2010), 720–723; Mat. Zametki 85, 5 (2009), 754–757. (2010) MR2572865
  5. Pan’zhenskii, V. I., Automorphisms of the Riemann–Cartan space-time manifold, . Tr. Mezhdunar. Geom. Tsentra 5, 2 (2012), 27–34. (2012) 
  6. Pan’zhenskii, V. I., Automorphisms of Riemann-Cartan Manifolds with Semi-Symmetric Connection, . Journal of Mathematical Physics, Analysis, Geometry 10, 2 (2014), 233–239. (2014) MR3236968
  7. Pan’zhenskii, V. I., 10.1134/S000143461509028X, . Math. Notes 98, 4 (2015), 613–623. (2015) Zbl1337.53045MR3438511DOI10.1134/S000143461509028X
  8. Yano, K., Bochner, S., Curvature and Betti Numbers, . Princeton Univ. Press, Princetton, NJ, 1953; Inostrannaya Literatura, Moscow, 1957. (1953) Zbl0051.39402MR0062505
  9. Stepanov, S. E., Gordeeva, I. A., 10.1134/S0001434610010311, . Math. Notes 87, 1-2 (2010), 248–257; Mat. Zametki 87, 2 (2010), 267–279. (2010) Zbl1197.53049MR2731477DOI10.1134/S0001434610010311

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