Related to Why symplectic geometry gives Poisson geometry

Is there any common use for the Lie bracket of the gradients of two functions? That is, $[\nabla f, \nabla g]$?

Here, $\nabla f$ denotes the vector field gotten by "raising the index" from $df$. In other words, $(\nabla f)(g) = m(df, dg)$, where $m$ is the Riemannian metric on some manifold.

Related to Why symplectic geometry gives Poisson geometry

Is there any common use for the Lie bracket of the gradients of two functions? That is, $[\nabla f, \nabla g]$?

Here, $\nabla f$ denotes the vector field gotten by "raising the index" from $df$. In other words, $(\nabla f)(g) = m(df, dg)$, where $m$ is the Riemannian metric on some manifold.

Related to Why symplectic geometry gives Poisson geometry

Is there any common use for the Lie bracket of the gradients of two functions? That is, $[\nabla f, \nabla g]$?

Related to Why symplectic geometry gives Poisson geometry

Is there any common use for the Lie bracket of the gradients of two functions? That is, $[\nabla f, \nabla g]$?

Here, $\nabla f$ denotes the vector field gotten by "raising the index" from $df$. In other words, $(\nabla f)(g) = m(df, dg)$, where $m$ is the Riemannian metric on some manifold.