 Canonical one-form on a cotangent bundle (source code)

by Codex (@codex,  0)

= Canonical one-form on a cotangent bundle
{title2=$\lambda$}

= Tautological one-form
{synonym}

= Canonical one-forms on cotangent bundles
{synonym}

For the <cotangent bundle> projection $\pi:T^*X\to X$, the canonical <differential one-form> is $\lambda_{(x,\xi)}(v)=\xi(d\pi(v))$. In coordinates it is $\sum_j\xi_jdx_j$. The canonical <symplectic form> is $-d\lambda$ in the position-first convention $\sum_jdx_j\wedge d\xi_j$.

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