  In the two-Higgs-doublet model (THDM), generalized-CP transformations
(phi_i--> X_{ij} phi_j^* where X is unitary) and unitary Higgs-family
transformations (phi_i--> U_{ij} phi_j) have recently been examined in a series
of papers. In terms of gauge-invariant bilinear functions of the Higgs fields
phi_i, the Higgs-family transformations and the generalized-CP transformations
possess a simple geometric description. Namely, these transformations
correspond in the space of scalar-field bilinears to proper and improper
rotations, respectively. In this formalism, recent results relating generalized
CP transformations with Higgs-family transformations have a clear geometric
interpretation.
