This paper investigates conformal invariance and conserved quantities of nonmaterial volumes. An infinitesimal transformation group and infinitesimal transformations vectors of generators are proposed. The definition of conformal invariance and the determining equation for the systems are presented. The necessary and sufficient conditions of conformal invariance being Noether symmetrical simultaneously by the action of infinitesimal transformations are given. The conformal factor is deduced from the conformal invariance and Noether symmetry. The corresponding Noether conserved quantities are derived with the aid of a structure equation. Three examples are given to illustrate application of the method, the corresponding conserved quantities are obtained under the conformal invariance and Noether symmetry.

中文翻译：

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非物质体积的共形不变性和守恒量

本文研究了非物质体积的共形不变性和守恒量。提出了生成元的无穷小变换群和无穷小变换向量。给出了共形不变性的定义和系统的确定方程。给出了保形不变性在无穷小变换作用下同时为诺特对称的充要条件。共形因子是从共形不变性和诺特对称性推导出来的。相应的诺特守恒量是借助结构方程推导出来的。给出了三个例子来说明该方法的应用，在共形不变性和Noether对称下得到了相应的守恒量。