Asymptotic behaviour of instantons on cylinder manifolds

Abstract

In this article, we study the instanton equation on the cylinder over a closed manifold X which admits non-zero smooth 3-form P and 4-form Q. Our results are (1) if X is a good manifold, i.e., P, Q satisfying $$d*_{X}P=d*_{X}Q=0$$, then the instanton with integrable curvature decays exponentially at the ends, and, (2) if X is a real Killing spinor manifold, i.e., P, Q satisfying $$dP=4Q$$ and $$d*_{X}Q=(n-3)*_{X}P$$, we prove that the solution of instanton equation is trivial under some mild conditions.