  We use the induced interaction of Babu and Brown to derive two novel
relations between the quasiparticle interaction in nuclear matter and the
unique low momentum nucleon-nucleon interaction V_low k in vacuum. These
relations provide two independent constraints on the Fermi liquid parameters of
nuclear matter. We derive the full renormalization group equations in the
particle-hole channels from the induced interaction. The new constraints,
together with the Pauli principle sum rules, define four combinations of Fermi
liquid parameters that are invariant under the renormalization group flow.
Using empirical values for the spin-independent Fermi liquid parameters, we are
able to compute the major spin-dependent ones by imposing the new constraints
and the Pauli principle sum rules. The effects of tensor forces are discussed.
