Some properties of para-Kahler-Walker metrics

ÖZKAN M., Iscan M.

ANNALES POLONICI MATHEMATICI, vol.112, no.2, pp.115-125, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 112 Issue: 2
  • Publication Date: 2014
  • Doi Number: 10.4064/ap112-2-2
  • Journal Name: ANNALES POLONICI MATHEMATICI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.115-125
  • Gazi University Affiliated: Yes

Abstract

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-Kahler-Walker manifolds. In particular, we obtain conditions under which these almost paracomplex structures are integrable, and the corresponding para-Kahler forms are symplectic. We also show that Petean's example of a nonflat indefinite Kahler-Einstein 4-manifold is a special case of our constructions.