  The effect of next-nearest-neighbor hopping $t_{2}$ on the ground-state phase
diagram of the one-dimensional Kondo lattice is studied with density-matrix
renormalization-group techniques and by comparing with the phase diagram of the
classical-spin variant of the same model. For a finite $t_{2}$, i.e., for a
zigzag-ladder geometry, indirect antiferromagnetic interactions between the
localized spins are geometrically frustrated. We demonstrate that $t_{2}$ at
the same time triggers several magnetic phases which are absent in the model
with nearest-neighbor hopping only. For strong $J$, we find a transition from
antiferromagnetic to incommensurate magnetic short-range order, which can be
understood entirely in the classical-spin picture. For weaker $J$, a
spin-dimerized phase emerges, which spontaneously breaks the discrete
translation symmetry. The phase is not accessible to perturbative means but is
explained, on a qualitative level, by the classical-spin model as well. Spin
dimerization alleviates magnetic frustration and is interpreted as a key to
understand the emergence of quasi-long-range spiral magnetic order which is
found at weaker couplings. The phase diagram at weak $J$, with gapless
quasi-long-range order on top of the two-fold degenerate spin-dimerized ground
state, competing with a nondegenerate phase with gapped spin (and charge)
excitations, is unconventional and eludes an effective low-energy spin-only
theory.
