Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry
УДК 514.764.2
Abstract
Currently, mathematical and computer modeling, as well as systems of symbolic calculations, are actively used in many areas of mathematics. Popular computer math systems as Maple, Mathematica, MathCad, MatLab allow not only to perform calculations using symbolic expressions but also solve algebraic and differential equations (numerically and analytically) and visualize the results. Differential geometry, like other areas of modern mathematics, uses new computer technologies to solve its own problems. The applying is not limited only to numerical calculations; more and more often, computer mathematics systems are used for analytical calculations. At the moment, there are many examples that prove the effectiveness of systems of analytical calculations in the proof of theorems of differential geometry.This paper demonstrates how symbolic computation packages can be used to classify neither conformally flat nor Ricci parallel four-dimensional Lie groups with leftinvariant (pseudo)Riemannian metric of the algebraic Ricci soliton with the zero Schouten-Weyl tensor.
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Komrakov B.B. Einstein-Maxwell equation on four-dimensional homogeneous spaces // Lobachevskii J. Math. 2001. V. 8.
Calvaruso G., Zaeim A. Conformally flat homogeneous pseudo-Riemannian four-manifolds // Tohoku Math. J. 2014. V. 66.
Calvaruso G., Zaeim A. Four-dimensional pseudo-Riemannian g.o. spaces and manifolds // Journal of Geometry and Physics. 2018. V. 130.
Calvaruso G., Fino A. Four-dimensional pseudo-Riemannian homogeneous Ricci solitions // International Journal of Geometric Methods in Modern Physics. 2011. V. 12, No 5.
Zaeim A., Haji-Badali A. Einstein-like Pseudo-Riemannian Homogeneous Manifolds of Dimension Four // Mediterranean Journal of Mathematics. 2016. V. 13(5).
Гладунова О.П., Славский В.В. О гармоничности тензора Вейля левоинвариантных римановых метрик на четырехмерных унимодулярных групах Ли // Математические труды. 2011. Т. 14. № 1.
Воронов Д.С., Родионов Е.Д. Левоинвариантные римановы метрики на четырехмерных неунимодулярных группах Ли с нулевой дивергенцией тензора Вейля // Доклады академии наук. 2010. Т. 432, № 3.
Gladunova O.P., Slavskii V.V. Harmonicity of the Weyl tensor of left-invariant Riemannian metrics on four-dimensional unimodular Lie groups // Siberian Advances in math. 2013. V. 23. № 1.
Гладунова О.П., Оскорбин Д.Н. Применение пакетов символьных вычислений к исследованию спектра оператора кривизны на метрических группах Ли // Известия Алтайского гос. ун-та. 2013. № 1/1(77).
Родионов Е.Д., Славский В.В., Чибрикова Л.Н. Локально конформно однородные псевдоримановы пространства // Математические труды. 2006. Т. 9. № 1.
Клепиков П.Н. Конформно плоские алгебраические солитоны Риччи на группах Ли // Математические заметки. 2018. Т. 104. № 1.
Клепиков П.Н. Четырехмерные метрические группы Ли с нулевым тензором Схоутена-Вейля // Сибирские электронные математические известия. 2019. Т. 16.
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