  In this paper, we extend a recent proposed model of two scalar and two vector
fields to a hyperbolic inflation scenario, in which the field space of two
scalar fields is a hyperbolic space instead of a flat space. In this model, one
of the scalar fields is assumed to be a radial field, while the other is set as
an angular field. Furthermore, both scalar fields will be coupled to two
different vector fields, respectively. As a result, we are able to obtain a set
of exact Bianchi type I solutions to this model. Stability analysis is also
performed to show that this set of anisotropic solutions is indeed stable and
attractive during the inflationary phase. This result indicates that the cosmic
no-hair conjecture is extensively violated in this anisotropic hyperbolic
inflation model.
