Bulletin of the
Korean Mathematical Society BKMS

We define an almost Norden submersion (holomorphic and semi-Riemannian submersion) between almost Norden manifolds and \linebreak show that, in most of the cases, the base manifold has the similar kind of structure as that of total manifold. We obtain necessary and sufficient conditions for almost Norden submersion to be a totally geodesic map. We also derive decomposition theorems for the total manifold of such submersions. Moreover, we study the harmonicity of almost Norden submersions between almost Norden manifolds and between Kaehler-Norden manifolds. Finally, we derive conditions for an almost Norden submersion to be a harmonic morphism.

Keywords: Almost Norden manifolds, Kaehler-Norden manifolds, holomorphic maps, almost Norden submersions, harmonic maps, totally geodesic maps, horizontally weakly conformal maps, harmonic morphisms

MSC numbers: Primary 53C42; Secondary 53C43, 53C15