The novel optical properties of wave propagation and the special feature of phot on geometric phases inside a noncoplanarly curved fiber made of biaxially anisot ropic left_handed media are considered in this paper. In general, the photon geo metric phases is inevitably dependent on the solid angle subtended by the curve along which the photon moves, which presents the topological and global property of time evolution of photon wavefunctions. It is, however, shown that inside a biaxially anisotropic left_handed fiber the photon geometric phases will be inde pendent of the cone angle, since the contributions of negative and positive refr active indices to the geometric phases of circularly polarized photons have been cancelled each other. In addition, we discuss briefly the properties of the qua ntum_vacuum geometric phases resulting from the quantum vacuum fluctuation, and the probability of the detection of such a vacuum effect in experiments.