  This series of papers is devoted to the study of deformations of Virasoro
symmetries of the principal hierarchies associated to semisimple Frobenius
manifolds. The main tool we use is a generalization of the bihamiltonian
cohomology called the variational bihamiltonian cohomology. In the present
paper, we give its definitions and compute the associated cohomology groups
that will be used in our study of deformations of Virasoro symmetries. To
illustrate its application, we classify the conformal bihamiltonian structures
with semisimple hydrodynamic limits.
