  We reveal the existence of a large in-plane heavy-hole $g$ factor in
symmetric self-assembled (001) (In,Ga)As/GaAs quantum dots due to warping of
valence band states. This warping dominates over the well-established mechanism
associated with a reduced symmetry of quantum dots and the corresponding mixing
of heavy-hole and light-hole states. The effect of band warping is manifested
in a unique angular dependence of a trion photon echo signal on the direction
of external magnetic field with respect to the sample axes. It results in a
uniform magnetic-field-induced optical anisotropy for the entire quantum dot
ensemble which is a prerequisite for realization of spin quantum memories and
spin-photon entanglement in the ensemble.
