Tractography is an important technique that allows the in vivo reconstruction of structural connections in the brain using diffusion MRI. Although tracking algorithms have improved during the last two decades, results of validation studies and international challenges warn about the reliability of tractography and point out the need for improved algorithms. In propagation-based tracking, connections have traditionally been modeled as piece-wise linear segments. In this work, we propose a novel propagation-based tracker that is capable of generating geometrically smooth ( C1 ) curves using parallel transport frames. Notably, our approach does not increase the complexity of the propagation problem that remains two-dimensional. Moreover, our tracker has a novel mechanism to reduce noise related propagation errors by incorporating topographic regularity of connections, a neuroanatomic property of many brain pathways. We ran extensive experiments and compared our approach against deterministic and other probabilistic algorithms. Our experiments on FiberCup and ISMRM 2015 challenge datasets as well as on 56 subjects of the Human Connectome Project show highly promising results both visually and quantitatively. Open-source implementations of the algorithm are shared publicly.