  A model with two curved compact extra dimensions is introduced. The model is
based on a four-brane immersed in a six dimensional space, where the extra
dimensions are compact but not flat. They have topology of torus. The form of
the metric in the empty bulk is studied and the gauge singlet fermion structure
showed to be very simple. It contain only one massless low energy mode which
couples to brane matter, while the massive modes are not related to the volume
of torus while the Planck mass is related to the volume of extra dimensions. In
the model "our" brane is situated on a nearly singular line of the torus.
