Basic function
= Basic function
{title2=$F=f\circ\pi$}
A basic function for a <Riemannian submersion> is a function pulled back from the base. It is constant along each <fiber>. Its <Riemannian gradient> is the <horizontal lift of a vector field through a submersion> of the base gradient. Constancy on connected fiber components alone need not imply global descent when fibers are disconnected.