  We report on a complex nontrivial behavior of the optical anisotropy of
quantum dots that is induced by a magnetic field in the plane of the sample. We
find that the optical axis either rotates in the opposite direction to that of
the magnetic field or remains fixed to a given crystalline direction. A
theoretical analysis based on the exciton pseudospin Hamiltonian unambiguously
demonstrates that these effects are induced by isotropic and anisotropic
contributions to the heavy-hole Zeeman term, respectively. The latter is shown
to be compensated by a built-in uniaxial anisotropy in a magnetic field B_c =
0.4 T, resulting in an optical response typical for symmetric quantum dots.
