  We show from real-space Hartree-Fock calculations within the extended Hubbard
model that next-nearest neighbor (t') hopping processes act to suppress the
formation of static charge stripes. This result is confirmed by investigating
the evolution of charge-inhomogeneous corral and stripe phases with increasing
t' of both signs. We propose that large t' values in YBCO prevent static stripe
formation, while anomalously small t' in LSCO provides an additional reason for
the appearance of static stripes only in these systems.
