The Group-Invariant CR Mappings between Spheres

Abstract

This thesis investigates CR mappings between spheres of minimal embedding dimension that are invariant under specific unitary subgroups classified by D’Angelo and Lichtblau. As background, we review established results for the (2n-1)-dimensional sphere for general n, as well as the improved upper bound for the minimal embedding dimension in the special case n=2. Building on this foundation, we develop and rigorously analyze new constructions of invariant CR mappings from the 5-sphere into higher-dimensional spheres, determining the exact minimal embedding dimension of the target space. These constructions expand the known family of minimal-dimension CR mappings and provide new insight into the relationship between group invariance and embedding dimension.