anisotropic case [@kunyang_aniso].

The motivation for studying the effect of anisotropy in FQHE is twofold. On the one hand, anisotropy probes the variations of the intrinsic metric of FQH fluids, a fundamental physical quantity that relates to the geometric description of FQHE. Secondly, we explore the possible effects resulting from tuning the rotational-symmetry breaking by an external parameter. Note that the rotational invariance is explicitly broken in real samples due to the presence of impurities, which are essential for the emergence of FQH plateaus. Furthermore, it is possible to induce the breaking of rotational invariance by tilting the magnetic field [@tilt], or by using systems with anisotropic bands, e.g. many-valley semiconductors like AlAs or Si in the presence of uniaxial stress. The former method is performed routinely and belongs to the most popular techniques for studying the FQHE; the latter method is relevant to AlAs [@shayegan] and some new classes of materials where FQHE might be studied. We provide brief arguments how the tilting of the field can be mapped to an effective variation of the metric, and then focus on the second method.

This paper is organized as follows. In Sec. \[sec\_model\] we introduce and motivate the model for 