A blow-up formula for stationary quaternionic maps

Let $(M, J^α, α=1,2,3)$ and $(N, {\cal J}^α, α=1,2,3)$ be Hyperkähler 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 $\lim_{k\to\infty}d(u_k^*{\cal J}^α)$, for $α=1,2,3$, 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 $d(u^*{\cal J}^α)=0$.

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