  In this paper, we study CR maps between hyperquadrics and Winkelmann
hypersurfaces. Based on a previous study on the CR Ahlfors derivative of
Lamel-Son and a recent result of Huang-Lu-Tang-Xiao on CR maps between
hyperquadrics, we prove that a transversal CR map from a hyperquadric into a
hyperquadric or a Winkelmann hypersurface extends to a local holomorphic
isometric embedding with respect to certain K\"ahler metrics if and only if the
Hermitian part of its CR Ahlfors derivative vanishes on an open set of the
source. Our proof is based on relating the geometric rank of a CR map into a
hyperquadric and its CR Ahlfors derivative.
