Kramers pair band geometry is quaternionic: a single positive-semidefinite quaternionic tensor unifies the quantum metric with the three SU(2) Berry curvatures and imposes metric-curvature bounds whose saturation defines ideal time reversal symmetric bands.
Riemannian structure on manifolds of quantum states,
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Quaternion-Kahler geometry of time reversal symmetric crystals
Kramers pair band geometry is quaternionic: a single positive-semidefinite quaternionic tensor unifies the quantum metric with the three SU(2) Berry curvatures and imposes metric-curvature bounds whose saturation defines ideal time reversal symmetric bands.