Zoll flows near Morse-Bott minima force the normal Hessian to be a compatible complex structure; in magnetic systems this produces almost Kähler metrics with constant corrected holomorphic sectional curvature, dynamically characterizing complex space forms.
Ginzburg and Ely Kerman
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On the Rigidity of Hamiltonians which are Zoll Near a Minimum, with an Application to Magnetic Systems and Almost-K\"ahler Manifolds
Zoll flows near Morse-Bott minima force the normal Hessian to be a compatible complex structure; in magnetic systems this produces almost Kähler metrics with constant corrected holomorphic sectional curvature, dynamically characterizing complex space forms.