Some properties of para-Kähler–Walker metrics

Tom 112 / 2014

Mustafa Özkan, Murat İşcan Annales Polonici Mathematici 112 (2014), 115-125 MSC: Primary 53C50; Secondary 53B30. DOI: 10.4064/ap112-2-2

Streszczenie

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.

Autorzy

  • Mustafa ÖzkanDepartment of Mathematics
    Faculty of Sciences
    Gazi University
    06500 Ankara, Turkey
    e-mail
  • Murat İşcanDepartment of Mathematics
    Faculty of Sciences
    Ataturk University
    25240 Erzurum, Turkey
    e-mail

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