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A framework is presented in this study which analyzes the importance of each sensor in an antenna array based on its location in the overall geometry. Moving away from the conventional methods of measuring sensor importance by means of application-specific criteria, a new approach, based on the array manifold and its differential geometry, is used to measure the significance of each sensor's position in an array. By considering two-dimensional manifolds (function of azimuth and elevation angles) of planar arrays of isotropic sensors, and by using previously established results on the differential geometry of such manifolds, a sensitivity analysis is performed which leads to characterization and quantification of sensor location importance in an array geometry. Based on this framework, a criterion is developed for assessing an overall geometry. This criterion may be used as a figure of merit for comparing diverse array geometries.