Einstein-like Pseudo-Riemannian Homogeneous Manifolds of Dimension Four

Zaeim, Amirhesam; Haji‐Badali, Ali

doi:10.1007/s00009-016-0696-6

Cited by 12 publications

(7 citation statements)

References 13 publications

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“…An Einstein-like metric and a commutative curvature operator over the homogenous four-manifold (M, g) were presented in [14] and [8], respectively. Here, we introduce a large class of some geometric examples in our classification of Theorem 3.1.…”

Section: Geometry Of Theorem 31mentioning

confidence: 99%

Recurrent curvature over four-dimensional homogeneous manifolds

Bastami¹,

Haji‐Badali²,

Zaeim³

2021

Revista De La Unión Matemática Argentina

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Section: Geometry Of Theorem 31mentioning

confidence: 99%

Recurrent curvature over four-dimensional homogeneous manifolds

Bastami¹,

Haji‐Badali²,

Zaeim³

2021

Revista De La Unión Matemática Argentina

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“…[3]. Стоит также отметить классификацию нетривиальных однородных инвариантных солитонов Риччи на четырехмерных локально однородных (псевдо)римановых многообразиях [4] и классификацию эйнштейново подобных метрик локально однородных псевдоримановых многообразий [5], получение которых напрямую использует системы компьютерной математики.…”

Section: Doiunclassified

Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry

Клепиков¹

2020

Известия АлтГУ

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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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“…Хромовой [3,4,5,6]. Эйнштейновоподобные однородные (псевдо)римановы 4-многообразия с нетривиальной подгруппой изотропии были классифицированы А. Заемом и А. Гаджи-Бадали в работе [7]. Классификация конформно плоских однородных (псевдо)римановых пространств (в том числе групп Ли) в четырехмерном случае была получена Дж.…”

Section: введение и предварительные сведенияunclassified

Four-dimensional metric Lie groups with zero Schouten–Weyl tensor

Клепиков¹

2019

Sib. Elektron. Mat. Izv.

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Einstein-like Pseudo-Riemannian Homogeneous Manifolds of Dimension Four

Cited by 12 publications

References 13 publications

Recurrent curvature over four-dimensional homogeneous manifolds

Recurrent curvature over four-dimensional homogeneous manifolds

Mathematical Modeling in Problems of Homogeneous (Pseudo)Riemaimian Geometry

Four-dimensional metric Lie groups with zero Schouten–Weyl tensor

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