Skip to main content
1 of 2
SoYu
  • 213
  • 1
  • 4

Any homogeneous symplectomorphism of tangent bundle $\dot{T}^*M=T^*M-0_M$ preserves the canonical Liouville form?

Let $\phi$ be a homogeneous symplectomorphism of tangent bundle $\dot{T}^*M=T^*M-0_M$ and let $\alpha_M$ be the canonical Liouville 1-form of $\dot{T}^*M$. Then is it true that $\phi^*\alpha_M=\alpha_M$?

SoYu
  • 213
  • 1
  • 4