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

Abstract

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.

References in corpus (2)

• Half conformally flat generalized quasi-Einstein manifolds
• The geometry of locally symmetric affine surfaces