Conformal Kaehler Euclidean submanifolds

Let f:M²ⁿ→R^2n+ℓ, n≥5, be a conformal immersion into Euclidean space with codimension ℓ where M²ⁿ is a Kaehler manifold of complex dimension n free of points where all sectional curvatures vanish. For codimension ℓ=1 or ℓ=2 we show that at least locally such a submanifold can always be obtained in a rather simple way, namely, from an isometric immersion of the Kaehler manifold M²ⁿ into either R²ⁿ⁺¹ or R²ⁿ⁺², the latter being a class of submanifolds already extensively studied.