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Dear authors! Submission of all materials is carried out only electronically through Online Submission System in personal account. DOI: 10.46698/f601708750171y On Conformal Factor in the Conformal Killing Equation on the 2Symmetric FiveDimensional Indecomposable Lorentzian Manifold
Andreeva, T. A. , Oskorbin, D. N. , Rodionov, E. D.
Vladikavkaz Mathematical Journal 2023. Vol. 25. Issue 3.
Abstract:
Conformally Killing vector fields are a natural generalization of Killing vector fields and play an important role in the study of the group of conformal transformations of a manifold, Ricci flows on a manifold, and the theory of Ricci solitons. PseudoRiemannian symmetric spaces of order \(k\), where \(k \geq 2\), arise in the study of pseudoRiemannian geometry and in physics. At present, they have been investigated in cases \(k=2, 3\) by D. V. Alekseevsky, A. S. Galaev and others. In the case of low dimensions, these spaces and Killing vector fields on them were studied by D. N. Oskorbin, E. D. Rodionov, and I. V. Ernst. Ricci solitons are a generalization of Einstein's metrics on (pseudo) Riemannian manifolds, and their equation has been studied on various classes of manifolds by many mathematicians. In particular, D. N. Oskorbin and E. D. Rodionov found a general solution of the Ricci soliton equation on 2symmetric Lorentzian manifolds of low dimension, and proved the local solvability of this equation in the class of 3symmetric Lorentzian manifolds. For a single Einstein constant in the Ricci soliton equation the Killing vector fields make it possible to find the general solution of the Ricci soliton equation corresponding to the given constant. However, for different values of the Einstein constant, conformally Killing vector fields play the role of Killing fields. Therefore, there is a need to study them. In this paper, we investigate the conformal analogue of the Killing equation on fivedimensional 2symmetric indecomposable Lorentzian manifolds, and investigate the properties of the conformal factor of the conformal analogue of the Killing equation on them. Nontrivial examples of conformally Killing vector fields with a variable conformal factor are constructed.
Keywords: conformal Killing vector fields, Lorentzian manifolds, \(k\)symmetric spaces, Killing vector fields, Ricci solitons
Language: Russian
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For citation: Andreeva, T. A., Oskorbin, D. N. and Rodionov, E. D. On Conformal Factor in the Conformal Killing Equation on the 2Symmetric FiveDimensional Indecomposable Lorentzian Manifold, Vladikavkaz Math. J., 2023, vol. 25, no. 3, pp. 514 (in Russian). DOI 10.46698/f601708750171y ← Contents of issue 
 

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