Applying the equivariant moving frames method, we construct a convergent normal form for real-analytic 5-dimensional totally nondegenerate submanifolds of \({\mathbb {C}}^4\). We develop this construction by applying further normalizations, the possibility of which completely relies upon vanishing/non-vanishing of some specific coefficients of the normal form. This in turn divides the class of our CR manifolds into several biholomorphically inequivalent subclasses, each of them has its own specified normal form with no further possible normalization applicable on it. It also is shown that, biholomorphically, Beloshapka’s cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.

应用等变运动框架方法，我们为\（{\ mathbb {C}} ^ 4 \）的实解析5维完全非退化子流形构造收敛范式。我们通过应用进一步的归一化来开发这种构造，这种归一化的可能性完全取决于法线形式的某些特定系数的消失/不消失。反过来，这将我们的CR流形的类别划分为几个双全不等价的子类，它们中的每一个都有其自己指定的范式，没有进一步适用的归一化方法。还表明，从全同构角度来看，贝洛沙普卡的三次模型是此类的唯一成员，具有无限小CR自同构的相应代数的最大可能维数7。我们的研究结果也可用于研究CR流形之间的双全等价问题。