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Unsupervised domain mapping aims to learn a function GXY to translate domain X to Y in the absence of paired examples. Finding the optimal GXY without paired data is an ill-posed problem, so appropriate constraints are required to obtain reasonable solutions. While some prominent constraints such as cycle consistency and distance preservation successfully constrain the solution space, they overlook the special properties of images that simple geometric transformations do not change the image's semantic structure. Based on this special property, we develop a geometry-consistent generative adversarial network (Gc-GAN), which enables one-sided unsupervised domain mapping. GcGAN takes the original image and its counterpart image transformed by a predefined geometric transformation as inputs and generates two images in the new domain coupled with the corresponding geometry-consistency constraint. The geometry-consistency constraint reduces the space of possible solutions while keep the correct solutions in the search space. Quantitative and qualitative comparisons with the baseline (GAN alone) and the state-of-the-art methods including CycleGAN [66] and DistanceGAN [5] demonstrate the effectiveness of our method.