Table of Contents
Geometry
Volume 2013, Article ID 373701, 6 pages
http://dx.doi.org/10.1155/2013/373701
Research Article

Symmetry Reduction of the Two-Dimensional Ricci Flow Equation

1School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 1684613114, Iran
2Department of Complementary Education, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran

Received 16 October 2012; Accepted 21 November 2012

Academic Editor: Salvador Hernandez

Copyright © 2013 Mehdi Nadjafikhah and Mehdi Jafari. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.