nLab horizontal differential form

Definition

There are two different meanings of horizontal differential form

Given a bundle $\pi \colon P \to X$ of smooth manifolds,

• then a differential form on the total space $P$ is horizontal if it vanishes on vertical vector fields:

• in the context of variational calculus:

  a differential form on the the total space $J^\infty_X(E)$ of the jet bundle of $E$ is horizontal if it is in the horizontal component of the variational bicomplex of $J^\infty(E)$.

Related concepts

• vertical differential form

• basic differential form

• variational bicomplex