  Through appropriate projections of an exact renormalization group equation,
we study fixed points, critical exponents and nontrivial renormalization group
flows in scalar field theories in $2<d<4$. The standard upper critical
dimensions $d_k={2k\over k-1}$, $k=2,3,4,\ldots$ appear naturally encoded in
our formalism, and for dimensions smaller but very close to $d_k$ our results
match the $\ee$-expansion. Within the coupling constant subspace of mass and
quartic couplings and for any $d$, we find a gradient flow with two fixed
points determined by a positive-definite metric and a $c$-function which is
monotonically decreasing along the flow.
