  Conforming materials to rigid substrates with Gaussian curvature --- positive
for spheres and negative for saddles --- has proven a versatile tool to guide
the self-assembly of defects such as scars, pleats, folds, blisters, and liquid
crystal ripples. Here, we show how curvature can likewise be used to control
material failure and guide the paths of cracks. In our experiments, and unlike
in previous studies on cracked plates and shells, we constrained flat elastic
sheets to adopt fixed curvature profiles. This constraint provides a geometric
tool for controlling fracture behavior: curvature can stimulate or suppress the
growth of cracks, and steer or arrest their propagation. A simple analytical
model captures crack behavior at the onset of propagation, while a
two-dimensional phase-field model with an added curvature term successfully
captures the crack's path. Because the curvature-induced stresses are
independent of material parameters for isotropic, brittle media, our results
apply across scales.
