On the Ricci Flow on Three-Dimensional Unimodular Lie Groups with Semisymmetric Equiaffine Connection
УДК 514.765
Abstract
Ricci flows play an important role in studies of geometry and topology of manifolds and were first studied for the Levi-Civita connection by R. Hamilton and other mathematicians. A natural generalization of the Levi-Civita connection is the class of metric connections with vector torsion, or the class of semisymmetric connections, first discovered by E. Cartan. The Ricci tensor of such connections is, generally speaking, not symmetric. Therefore, when studying Ricci flows for semisymmetric connections, it is necessary to consider semisymmetric equiaffine connections, or such semisymmetric connections for which the Ricci tensor is symmetric. In the case of Lie groups, this is equivalent to the fulfillment of a certain system of algebraic equations.
In this paper, we study the Ricci flow on three-dimensional unimodular Lie groups with a semisymmetric equiaffine connection. The flow equation in the coordinate system of J. Milnor is reduced to a mixed system consisting of algebraic and differential equations. By solving a subsystem of algebraic equations and substituting the obtained solutions into a subsystem of differential equations, we find the Ricci flow on a three-dimensional unimodular Lie group with the Milnor metric with respect to a se-misymmetric equiaffine connection.
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References
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Copyright (c) 2026 Данила Сергеевич Григорьев, Дмитрий Николаевич Оскорбин, Евгений Дмитриевич Родионов
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