Some properties of para-Kähler–Walker metrics

Mustafa Özkan¹ ; Murat İşcan²

¹ Department of Mathematics Faculty of Sciences Gazi University 06500 Ankara, Turkey
² Department of Mathematics Faculty of Sciences Ataturk University 25240 Erzurum, Turkey

Annales Polonici Mathematici, Tome 112 (2014) no. 2, pp. 115-125

Résumé

A Walker $4$-manifold is a pseudo-Riemannian manifold $(M_{4} ,g)$ of neutral signature, which admits a field of parallel null $2$-planes. We study almost paracomplex structures on $4$-dimensional para-Kähler–Walker manifolds. In particular, we obtain conditions under which these almost paracomplex structures are integrable, and the corresponding para-Kähler forms are symplectic. We also show that Petean's example of a nonflat indefinite Kähler-Einstein $4$-manifold is a special case of our constructions.

Détail

DOI : 10.4064/ap112-2-2

Mots-clés : walker manifold pseudo riemannian manifold neutral signature which admits field parallel null planes study almost paracomplex structures dimensional para k hler walker manifolds particular obtain conditions under which these almost paracomplex structures integrable corresponding para k hler forms symplectic peteans example nonflat indefinite hler einstein manifold special constructions