Geometry and Topology

About the Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection

D. S. Grigoryev, D. N. Oskorbin, E. D. Rodionov

Altai State University, Barnaul

Abstract: The Ricci flow on three-dimensional non-unimodular Lie groups with semisymmetric equiaffine connection is studied. The Ricci flow equation in the coordinate system proposed by J. Milnor is reduced to systems of algebraic and differential equations. A solution to the Ricci flow equation in the class of left-invariant Milnor metrics is found. The results of works by K. Onda, D. Knopf and K. McLeod concerning the Ricci flow on three-dimensional Lie groups in the case of Levi-Civita connectivity are generalised.

Keywords: Ricci flow; three-dimensional non-unimodular Lie groups; semisymmetric equiaffine connections.

UDC: 514.765