  Applications of non-Riemannian acoustic geometries in Bose-Einstein
condensates (BEC) are considered. The first is the Minkowski-Cartan
irrotational vortex acoustic geometry of nonlinear Schr\"{o}dinger equations of
BEC (Gross-Pitaeviskii (GP) equation). In this model, which is an alternative
to the Riemannian acoustic geometry of phonons in BEC, the Cartan acoustic
torsion is physically interpreted as the bending of the BEC wave function
amplitude. Actually this shows that acoustic torsion is given by the density
perturbation of BEC flow as happens in relativistic cosmological fluid
spacetimes. The Ricci-Cartan curvature scalar is computed and a torsion
singularity is found at the origin of a quantized vortex in BEC. In the second
example, a transverse Magnus force is shown to be expressed in terms of
acoustic torsion on a teleparallel vortex acoustics geometry.
