The topic of outlier detection in sensor networks has received significant attention in recent years. Detecting when the measurements of a node become "abnormal'' is interesting, because this event may help detect either a malfunctioning node, or a node that starts observing a local interesting phenomenon (i.e., a fire). In this paper we present a new algorithm for detecting outliers in sensor networks, based on the geometric approach. Unlike prior work. our algorithms perform a distributed monitoring of outlier readings, exhibit 100% accuracy in their monitoring (assuming no message losses), and require the transmission of messages only at a fraction of the epochs, thus allowing nodes to safely refrain from transmitting in many epochs. Our approach is based on transforming common similarity metrics in a way that admits the application of the recently proposed geometric approach. We then propose a general framework and suggest multiple modes of operation, which allow each sensor node to accurately monitor its similarity to other nodes. Our experiments demonstrate that our algorithms can accurately detect outliers at a fraction of the communication cost that a centralized approach would require (even in the case where the central node lies just one hop away from all sensor nodes). Moreover, we demonstrate that these bandwidth savings become even larger as we incorporate further optimizations in our proposed modes of operation.