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Unmanned Aerial Vehicles (UAVs) have rapidly become popular for monitoring, delivery, and actuation in many application domains such as environmental management, disaster mitigation, homeland security, energy, transportation, and manufacturing. However, the UAV perception and navigation intelligence (PNI) designs are still in their infancy and demand fundamental performance and energy optimizations to be eligible for mass adoption. In this article, we present a generalizable three-stage optimization framework for PNI systems that (i) abstracts the high-level programs representing the perception, mining, processing, and decision making of UAVs into complex weighted networks tracking the interdependencies between universal low-level intermediate representations; (ii) exploits a differential geometry approach to schedule and map the discovered PNI tasks onto an underlying manycore architecture. To mine the complexity of optimal parallelization of perception and decision modules in UAVs, this proposed design methodology relies on an Ollivier-Ricci curvature-based load-balancing strategy that detects the parallel communities of the PNI applications for maximum parallel execution, while minimizing the inter-core communication; and (iii) relies on an energy-aware mapping scheme to minimize the energy dissipation when assigning the communities onto tile-based networks-on-chip. We validate this approach based on various drone PNI designs including flight controller, path planning, and visual navigation. The experimental results confirm that the proposed framework achieves 23% flight time reduction and up to 34% energy savings for the flight controller application. In addition, the optimization on a 16-core platform improves the on-time visit rate of the path planning algorithm by 14% while reducing 81% of run time for ConvNet visual navigation.