Quadratic homogeneous polynomial maps $H$ and Keller maps $x+H$ with $rk JH=3$

Abstract: We classify all quadratic homogeneous polynomial maps $H$ and Keller maps of the form $x + H$, for which $rk J H = 3$, over a field $K$ of arbitrary characteristic. In particular, we show that such a Keller map (up to a square part if $char K=2$) is a tame automorphism.