This paper studies autonomous synchronization of k agent orientations is an element of SO(n) by using links that each convey (a priori different) partial state information between two agents: the latter compare the action of their states on a common link-dependent vector of R-n. Such setting appears when each pair of agents compares the expression, in their respective body frames, of a common external direction (force field, heading of moving object, etc.). To synchronize their states, agents must combine this information over time or throughout the network. A gradient coupling law for synchronization is proposed. Extensive convergence analysis of the coupled agents is provided, both for fixed and time-varying reference vectors. The results are compared to a similar setting with states in R-n and agents coupled through scalar product of their state with a reference vector.