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Symmetry Reduction of the Two-Dimensional Ricci Flow Equation

Research paper by Mehdi Nadjafikhah, Mehdi Jafari

Indexed on: 31 Jul '14Published on: 31 Jul '14Published in: Mathematics - Differential Geometry



Abstract

This paper is devoted to obtain the one-dimensional group invariant solutions of the two-dimensional Ricci flow ((2D) Rf) equation. By classifying the orbits of the adjoint representation of the symmetry group on its Lie algebra, the optimal system of one-dimensional subalgebras of the ((2D) Rf) equation is obtained. For each class, we will find the reduced equation by the method of similarity reduction. By solving these reduced equations, we will obtain new sets of group invariant solutions for the ((2D) Rf) equation.