On Levi‐flat hypersurfaces with singularities on a manifold boundary

Abstract We study germs of real‐analytic Levi‐flat hypersurfaces with singularities on a boundary manifold. We prove the existence of a normal form for a real‐analytic Levi‐flat hypersurface which is defined by the vanishing of the real part of , , and singularities. Finally, we prove a version of Morse–Vey's lemma for a real‐analytic Levi‐flat hypersurface with singularities on the boundary.