Application of Symbolic Computation Packages for Investigation of Algebraic Ricci Solitons in Homogeneous (Pseudo)Riemannian Manifolds

Клепиков, Павел Николаевич; Родионов, Евгений Дмитриевич

doi:10.14258/izvasu(2017)4-19

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2023

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Cited by 2 publications

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“…Далее приведем математическую модель, позволяющую вычислять квадрат длины тензора Вейля на локально однородном (псевдо)римановом пространстве (подробнее см. [9,10]).…”

Section: Introductionunclassified

The Isotropic Weyl Tensor on Four-Dimensional Locally Homogeneous Pseudo-Riemannian Manifolds

Клепикова¹

2019

izvasu

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Section: Introductionunclassified

The Isotropic Weyl Tensor on Four-Dimensional Locally Homogeneous Pseudo-Riemannian Manifolds

Клепикова¹

2019

izvasu

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Eigenvalues of Ricci Operator of Four-Dimensional Locally Homogeneous Riemannian Manifolds with Nontrivial Isotropy Subgroup

Клепиков¹,

Родионов²

2023

Известия АлтГУ

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The topology of Riemannian manifolds can be linked to the eigenvalues of curvature operators, which was demonstrated in the works of J. Milnor, V.N. Berestovsky, V.V. Slavkii, E.D. Rodionov, and Yu.G. Nikonorov. J. Milnor studied the eigenvalues of the Ricci curvature operator of left-invariant Riemannian metrics on Lie groups, and identified possible signatures of the Ricci operator for three-dimensional Lie groups. O. Kowalski and S. Nikcevic later resolved the problem of prescribed spectrum values of the Ricci operator on three-dimensional metric Lie groups and Riemannian locally homogeneous spaces. D.N. Oskorbin, E.D. Rodionov, and O.P. Khomova also obtained similar results for the one-dimensional curvature operator and the sectional curvature operator. A.G. Kremlev and Yu.G. Nikonorov investigated the fourdimensional case and studied the possible signatures of the Ricci curvature of left-invariant Riemannian metrics on Lie groups. In this study, we aim to solve the problem of prescribed eigenvalues of the Ricci operator on locally homogeneous Riemannian manifolds with a nontrivial isotropy subgroup.

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Application of Symbolic Computation Packages for Investigation of Algebraic Ricci Solitons in Homogeneous (Pseudo)Riemannian Manifolds

Cited by 2 publications

References 4 publications

The Isotropic Weyl Tensor on Four-Dimensional Locally Homogeneous Pseudo-Riemannian Manifolds

The Isotropic Weyl Tensor on Four-Dimensional Locally Homogeneous Pseudo-Riemannian Manifolds

Eigenvalues of Ricci Operator of Four-Dimensional Locally Homogeneous Riemannian Manifolds with Nontrivial Isotropy Subgroup

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