  We suggest a conformally invariant generalization of string theory to
higher-dimensional objects. As such a model, we consider a conformally
invariant $\sigma$ model. For this theory, the Hamiltonian formalism is
constructed, and the full set of constraints is found. The equations obtained
are studied under a fixed gauge. It is shown that special cases of the model
are string theory and Einstein's theory of gravity. Cosmological application of
the suggested theory are studied. It is shown that Friedmann-like models can be
described in this framework. Our models make it possible to interpret the
Universe evolution as evolution of three-dimensional objects embedded in a
higher-dimensional flat space-time.
