Isomorphisms of trees

Let $\kappa$ , $\lambda$ be cardinals, $\kappa \ge {\mathrm{\aleph }}_1$ and regular, and $2\le \lambda \le \kappa$ . If $\kappa >{\mathrm{\aleph }}_1$ and $\lambda >\kappa$ , and if there is a $\kappa$ -Suslin ( $\kappa$ -Aronszajn, $\kappa$ -Kurepa) tree, then there are $2^{\kappa }$ normal $\lambda$ -ary rigid nonisomorphic $\kappa$ -Suslin ( $\kappa$ -Aronszajn, $\kappa$ -Kurepa) trees. If there is a Suslin (Aronszajn, Kurepa) tree, then there is a normal rigid Suslin (Aronszajn, Kurepa) tree. If there is a $\kappa$ -Canadian tree, then there are $2^{\kappa }$ normal $\lambda$ -ary rigid nonisomorphic $\kappa$ -Canadian trees.