  Due to its p-like character, the valence band in GaAs-based heterostructures
offers rich and complex spin-dependent phenomena. One manifestation is the
large anisotropy of Zeeman spin splitting. Using undoped, coupled quantum wells
(QWs), we examine this anisotropy by comparing the hole spin dynamics for high-
and low-symmetry crystallographic orientations of the QWs. We directly measure
the hole $g$ factor via time-resolved Kerr rotation, and for the low-symmetry
crystallographic orientations (110) and (113a), we observe a large in-plane
anisotropy of the hole $g$ factor, in good agreement with our theoretical
calculations. Using resonant spin amplification, we also observe an anisotropy
of the hole spin dephasing in the (110)-grown structure, indicating that
crystal symmetry may be used to control hole spin dynamics.
