  We study a frustrated antiferromagnetic isotropic Heisenberg $S=1$ chain
using a variational ansatz and the DMRG. At $\alpha_D=0.284(1)$, there is a
disorder point of the second kind, marking the onset of incommensurate
correlations in the chain. At $\alpha_L=0.3725(25)$ there is a Lifshitz point,
at which the excitation spectrum develops a doubly degenerate structure. These
points are the quantum remnants of the transition from antiferromagnetic to
spiral order in the classical frustrated chain. At $\alpha_T=0.7444(6)$ there
is a first order phase transition from an AKLT phase to a next-nearest neighbor
generalization of the AKLT model. At the transition, the string order parameter
shows a discontinuous jump of 0.085 to 0; the correlation length and the gap
are both finite at the transition. The problem of edge states in open
frustrated chains is discussed at length.
