A conformal invariance for generalized Birkhoff equations

In this article, generalized Birkhoff equations are put forward by adding supplementary terms to the Birkhoff equations. A conformal invariance of the Birkhoff equations can be used to study the generalized Birkhoff Equations, and two examples are presented to illustrate the application of the results. The project supported by the National Natural Science Foundation of China (10572021 and 10772025) and the Doctoral Program Foundation of Institution of Higher Education, China (20040007022). The English text was polished by Yunming Chen.