扭曲乘积形式的2维双曲Yamabe方程

2-Dimensional Hyperbolic Yamabe Equation in Form of Warped Products

本文通过扭曲乘积流形中一种特殊的度量形式,即旋转对称度量,研究了2维双曲空间在扭曲乘积R_(+)×_(φ)S^(1)形式下的Yamabe方程,推导出了扭曲乘积形式的标准单位球面的Yamabe方程及其解,并在此基础上,通过类比找到了2维双曲Yamabe方程的一组特解.

In this paper,the Yamabe Equation of 2-dimensional hyperbolic space in the form of R_(+)×_(φ)S^(1) is studied in a special form of warped products,that is,the metric of rotational symmetry.The Yamabe Equation and its solution of the standard unit sphere in the form of warped product are derived.On this basis,a set of special solutions of the 2-dimensional hyperbolic Yamabe Equation are found by analogy.