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

John Douglas Moore
2021 Annals of Global Analysis and Geometry  
AbstractThis 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.
doi:10.1007/s10455-021-09771-8 fatcat:4yfjcooqurbwjhqyt7jssvlkxa