On normal forms of complex points of small C²-perturbations of real 4-manifolds embedded in a complex 3-manifold

Abstract

We answer the question how arbitrarily small perturbations of a pair of one arbitrary and one symmetric 2 × 2 matrix can change a normal form with respect to a certain linear group action. This result is then applied to describe the quadratic part of normal forms of complex points of small C 2 -perturbations of real 4-manifolds embedded in a complex 3-manifold.