In this paper we address the general problem of including inflationary models
exhibiting Starobinsky-like potentials into (symmetric) N=2
supergravities. This is done by gauging suitable abelian isometries of the
hypermultiplet sector and then truncating the resulting theory to a single
scalar field. By using the characteristic properties of the global symmetry
groups of the N=2 supergravities we are able to make a general
statement on the possible α-attractor models which can obtained upon
truncation. We find that in symmetric N=2 models group theoretical
constraints restrict the allowed values of the parameter α to be
α=1,32,31. This confirms and generalizes results
recently obtained in the literature. Our analysis heavily relies on the
mathematical structure of symmetric N=2 supergravities, in
particular on the so called c-map connection between Quaternionic K\"ahler
manifolds starting from Special K\"ahler ones. A general statement on the
possible consistent truncations of the gauged models, leading to
Starobinsky-like potentials, requires the essential help of Tits Satake
universality classes. The paper is mathematically self-contained and aims at
presenting the involved mathematical structures to a public not only of
physicists but also of mathematicians. To this end the main mathematical
structures and the general gauging procedure of N=2 supergravities
is reviewed in some detail.Comment: 101 pages, LaTeX sourc