Geometric Resonance in Modulated Quantum Hall Systems Near $ \nu = 1/2$

We propose a theory for the new effects recently observed by Willett et al [1] in the magnetoresistance of a weakly modulated two dimensional electron gas near filling factor 1/2. Minima in transverse magnetoresistance and maxima in longitudinal magnetoresistance at the same magnetic field producing the new resonance structure are reported. The structure occurs due to geometric resonance of the composite fermion cyclotron orbits with the modulation period of the effective magnetic field $B_{eff}$ due to the applied density modulation. The transverse minimum occurs due to the inhomogeneity in the field $B_{eff}$ in the presence of density modulations, whereas the longitudinal maximum can arise due to a shape-effect (distortion) of the composite fermion Fermi surface (CF-FS). Thus the minima and maxima reflect different physical mechanisms. PACS numbers 71.10 Pm, 73.40 Hm, 73.20 Dx {}