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phlegmax
phlegmax
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Consider a Kähler manifold with complex structure $J$. Is there a characterization of real-valued functions $H$ for which the corresponding Hamiltonian vector field $X_H$ is real-holomorphic, that is, $\mathscr{L}_{X_H}J=0$ ?

Stated differently, is it possible to characterize energy functions on Kähler manifolds that give rise to isometric Hamiltonian dynamics?

Consider a Kähler manifold with complex structure $J$. Is there a characterization of real-valued functions $H$ for which the corresponding Hamiltonian vector field $X_H$ is real-holomorphic, that is, $\mathscr{L}_{X_H}J=0$ ?

Consider a Kähler manifold with complex structure $J$. Is there a characterization of real-valued functions $H$ for which the corresponding Hamiltonian vector field $X_H$ is real-holomorphic, that is, $\mathscr{L}_{X_H}J=0$ ?

Stated differently, is it possible to characterize energy functions on Kähler manifolds that give rise to isometric Hamiltonian dynamics?

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phlegmax
phlegmax
  • 121
  • 2

Real-holomorphic Hamiltonian vector fields

Consider a Kähler manifold with complex structure $J$. Is there a characterization of real-valued functions $H$ for which the corresponding Hamiltonian vector field $X_H$ is real-holomorphic, that is, $\mathscr{L}_{X_H}J=0$ ?