Self-intersections of closed parametrized minimal surfaces in generic Riemannian manifolds

This article shows that for generic choice of Riemannian metric on a compact oriented manifold M of dimension four, the tangent planes at any self-intersection $$p \in M$$ p ∈ M of any prime closed parametrized minimal surface in M are not simultaneously complex for any orthogonal complex structure on M at p. This implies via geometric measure theory that $$H_2(M;{{\mathbb {Z}}})$$ H 2 ( M ; Z ) is generated by homology classes that are represented by oriented imbedded minimal surfaces.