On regular Stein neighborhoods of a union of two maximally totally real subspaces in C-n

摘要

We construct regular Stein neighborhoods of a union of two maximally totally real subspaces M = (A + i I) Rn and N = Rn in Cn, provided that the eigenvalues of the real n x n matrix A are sufficiently small. This result is applied to provide regular Stein neighborhoods of an immersed totally real n-manifold in a complex n-manifold, with only finitely many double points, and such that the union of the tangent spaces at each double point in some local coordinates coincides with M. N, described above.