A blow-up formula for stationary quaternionic maps

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 \(d(u^*{\cal J}^\alpha)=0\).