Affine surfaces which are Kähler, para-Kähler, or nilpotent Kähler

الأصل · EN

Motivated by the construction of Bach flat neutral signature Riemannian extensions, we study the space of parallel trace free tensors of type (1,1) on an affine surface. It is shown that the existence of such a parallel tensor field is characterized by the recurrence of the symmetric part of the Ricci tensor.