Karina Słuka (Institute of Mathematics, Wrocław University of Technology, Poland)

PROPERTIES OF THE CURVATURE OF KÄHLER-NORDEN MANIFOLDS

ABSTRACT

Let M be a smooth 2n-dimensional manifold with an almost complex structure J and a pseudo-Riemannian anti-Hermitian metric g, i.e.

J^{2} = −I, g(JX, JY) = −g(X, Y).

If additionaly ∇J = 0, where ∇ is the Levi-Civita connection of g, then the triple (M, J, g) form a Kähler-Norden manifold. A structure of this kind is also called an almost complex structure with B-metric, or an anti-Kählerian structure.

We have considered the classes of Kähler-Norden manifolds with recurrent curvature, recurrent holomorphic projective curvature, or recurrent conformal curvature.

We are also interested in those Kähler-Norden manifolds satisfying the conditions of semisymmetry or more generally the conditions of pseudosymmetry type.