  Haldane's geometrical description of fractional quantum Hall states is
generalized to compressible states. It is shown that anisotropy in the
composite fermion Fermi surface is a direct reflection of this intrinsic
geometry. A simple model is introduced in which the geometric parameter can be
obtained exactly from other parameters including electron mass anisotropy. Our
results compare favorably with recent measurements of anisotropy in composite
fermion Fermi surface [D. Kamburov, Y. Liu, M. Shayegan, L. N. Pfeiffer, K. W.
West, and K. W. Baldwin, Phys. Rev. Lett. 110, 206801 (2013)]. Broader
implications of our results are discussed.
