On the curvature of CR-structures and it covariant derivatives (Q1088821)

In \textit{S. S. Chern} and \textit{J. K. Moser}'s Erratum [Usp. Mat. Nauk 38, No.2(230), 149-193 (1983), translation of the English original from Acta Math. 133 (1974), 219-271 (1975; Zbl 0302.32015)] errors about changing coefficients of Moser's normal form in \({\mathbb{C}}^ 2\) under linear fractional transformations were pointed out. The main purpose of this article is that, using the method of moving frames, we retrieve the correct change of coefficients in Moser's normal form again by relating Chern's curvature and its suitably defined covariant derivatives to the normal form up to certain weight. Some formulae may be viewed as complements to Chern and Moser's distinguished article.