On the Cartan-Norden theorem for affine Kähler immersions

Abstract

In [O2] the Cartan-Norden theorem for real affine immersions was proved without the non-degeneracy assumption. A similar reasoning applies to the case of affine Kähler immersions with an anti-complex shape operator, which allows us to weaken the assumptions of the theorem given in [NP]. We need only require the immersion to have a non-vanishing type number everywhere on M .