This paper presents a methodology for computation of artificial vector fields that allows a robot to converge to and circulate around generic curves specified in $n$ -dimensional spaces. These vector fields may be directly applied to solve several robot-navigation problems such as border monitoring, surveillance, target tracking, and multirobot pattern generation, with special application to fixed-wing aerial robots, which must keep a positive forward velocity and cannot converge to a single point. Unlike previous solutions found in the literature, the approach is based on fully continuous vector fields and is generalized to time-varying curves defined in $n$-dimensional spaces. We provide mathematical proofs and present simulation and experimental results that illustrate the applicability of the proposed approach. We also present a methodology for construction of the target curve based on a given set of its samples.