  In this paper, we present infinitely many conserved densities satisfying
particular conservation law $F_{t}=(2uF)_{x}$ for the generalized Riemann
equations at $N=2,3,4$. In the $N=2$ case, we also construct conserved
densities corresponding to new conservation laws containing an arbitrary smooth
function. In virtue of reductions and/or changes of variables, related
conserved densities are obtained for two component Hunter-Saxton equation,
Hunter-Saxton equation, Gurevich-Zybin equation and Monge-Ampere equation.
