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Isotropic sections and curvature properties of hyperbolic Kaehlerian manifolds. (English) Zbl 0587.53026
The authors prove a series of theorems relating to the sectional curvature of a so-called hyperbolic Kählerian manifold, i.e. a pseudo- Riemannian manifold (M,g) with a parallel (1,1)-tensor field P satisfying the conditions \[ P^ 2=I,\quad g(PX,PY)+g(X,Y)=0. \] In particular they give characterizations of such spaces of constant holomorphic sectional curvature and of Bochner flat spaces and they also consider the axioms of 2-planes. They follow closely the methods for the case of Kähler manifolds but here the theorems are slightly more complicated because of the existence of different kind of plane sections.
Reviewer: L.Vanhecke

MSC:
53B30 Local differential geometry of Lorentz metrics, indefinite metrics
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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