Let $(M, J^\alpha, \alpha =1,2,3)$ and $(N, { \cal J}^\alpha, \alpha =1,2,3)$ be Hyperk\"ahler manifolds. Suppose that $u_k$ is a sequence of stationary quaternionic maps and converges weakly to $u$ in $H^{ 1,2}(M,N)$, we derive a blow-up formula for $\lim_{ k\to\infty}d(u_k^*{ \cal J}^\alpha)$, for $\alpha=1,2,3$, in the weak sense. As a corollary, we show that the maps constructed by Chen-Li [CL2] and by Foscolo [F] can not be tangent maps (c.f [LT], Theorem 3.1) of a stationary quaternionic map satisfing $d(u^*{ \cal J}^\alpha)=0$.
Categories: math.DG