Neural geometry in the human hippocampus enables generalization across spatial position and gaze.
Hippocampal neurons track the positions of self, others, and gaze direction. However, it is unclear how their respective neural codes differ enough to avoid confusion while allowing for abstraction across spatial frames. We recorded from populations of hippocampal neurons while human participants performed a joystick-controlled virtual prey-pursuit task. We found that neurons have mixed selective responses that map the positions of self, prey, and predator, as well as gaze direction. Their codes occupied mostly orthogonal subspaces, but the geometric structures of these subspaces allowed them to be aligned by simple linear transformations. Moreover, their geometries supported some degree of generalization, such that a linear rule learned on one agent could be transferred to another. This scheme enables reliable individuation and abstraction across both agent identity and viewpoint. Together, these findings suggest that hippocampal spatial knowledge is structured as a family of geometrically related manifolds that can be related through simple linear transformations.