Affine surfaces which are K\"ahler, para-K\"ahler, or nilpotent K\"ahler

E. Calvi\~no-Louzao; E. Garc\'ia-R\'io; I. Guti\'errez-Rodr\'iguez; P. Gilkey; R. V\'azquez-Lorenzo

arxiv: 1801.08306 · v1 · pith:OOVMLHCNnew · submitted 2018-01-25 · 🧮 math.DG

Affine surfaces which are K\"ahler, para-K\"ahler, or nilpotent K\"ahler

E. Calvi\~no-Louzao , E. Garc\'ia-R\'io , P. Gilkey , I. Guti\'errez-Rodr\'iguez , R. V\'azquez-Lorenzo This is my paper

classification 🧮 math.DG

keywords ahleraffineparalleltensorbachcharacterizedconstructionexistence

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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.

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Affine surfaces which are K\"ahler, para-K\"ahler, or nilpotent K\"ahler

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