CLASSIFICATION OF HOLOMORPHIC MAPPINGS OF HYPERQUADRICS FROM C2 TO C3

Abstract. We give a new proof of Faran’s and Lebl’s results by means of a new CR-geometric approach and classify all holomorphic mappings from the sphere in C2 to Levi-nondegenerate hyperquadrics in C3. We use the tools developed by Lamel, which allow us to isolate and study the most interesting class of holomorphic mappings. This family of so-called nondegenerate and transversal maps we denote by F. For F we introduce a subclass N of maps which are normalized with respect to the group G of automorphisms fixing a given point. With the techniques introduced by Baouendi–Ebenfelt–Rothschild and Lamel we classify all maps in N. This intermediate result is crucial to obtain a complete classification of F by considering th