Geometry-Aware Networking for Low-Altitude Economy: Movable Antennas in Space-Air-Ground Integrated Systems

Space--air--ground integrated networks (SAGINs) are emerging as a key foundation for future non-terrestrial networks (NTNs) and low-altitude economy services. However, their performance is increasingly limited not only by communication resources, but by the inability to adapt to rapidly changing spatial geometry. Here, spatial geometry refers to the relative configuration among network nodes, obstacles, and targets, which directly determines propagation conditions, blockage states, interference patterns, and sensing observability.This trend becomes more pronounced as low-altitude operations grow in density and complexity, causing the dominant bottleneck to shift from static resource allocation toward real-time maintenance of favorable spatial geometry across layers.In this article, we argue that movable antenna (MA) technology provides a fundamentally new perspective for SAGIN design. By enabling controlled antenna displacement, MA introduces a spatial degree of freedom that allows the network to directly adapt local spatial geometry at fine granularity, rather than passively reacting to it through beamforming or platform mobility.We present a geometry-aware, layered SAGIN architecture, where Low-Earth-Orbit (LEO) provides macro-scale coverage and coordination, High-Altitude Platform Stations (HAPS) enables regional continuity and backhaul support, and MA is incorporated into the layered design to enable fine-grained geometry adaptation, particularly at unmanned aerial vehicles (UAVs) and terrestrial layers where local channel dynamics are most pronounced. We further discuss how such geometry control enhances robustness, supports multi-functional operation spanning communication, sensing, control, and navigation, and enables more flexible spatial cooperation across layers.