Light detection and ranging (LIDAR) is a valuable tool for mapping vegetation structure in dense forests. Although several LIDAR-derived metrics have been proposed for characterizing vertical forest structure in previous studies, none of these metrics explicitly measure open space, or vertical gaps, under a forest canopy. We develop new LIDAR metrics that characterize vertical gaps within a forest for use in forestry and forest management applications. The proposed metrics are extracted from discrete return LIDAR data acquired over the La Selva Biological Station, Costa Rica across three different forest management types (old-growth, secondary-growth, and selectively-logged). A comparison to common LIDAR metrics of vertical vegetation structure revealed that our new metrics provide unique information about the structure of the forest canopy. Maps showing the distribution of vertical gap and complex canopy patches identified from our LIDAR metrics demonstrate that the pattern of open space in tropical rain forests is linked to forest management strategies.