We consider almost Kenmotsu manifolds with conformal Reeb foliation. We prove that such a foliation produces harmonic morphisms,we study the k-nullity distributions and we discuss the isometric immersion of such a manifold M as hypersurface in a real space form M(c) of constant curvature c proving that c is less or equal to −1 and,if c<−1, M is totally umbilical, Kenmotsu and locally isometric to the hyperbolic space of constant curvature −1. Finally, the Einstein and \eta-Einstein conditions are discussed. 2000Mathematics Subject Classification : 53C15; 53C25. Key words and phrases : Almost Kenmotsu manifolds, harmonic morphisms, nullity distributions, real space forms, \eta-Einstein conditions.

### Almost Kenmotsu manifolds with conformal Reeb foliation

#### Abstract

We consider almost Kenmotsu manifolds with conformal Reeb foliation. We prove that such a foliation produces harmonic morphisms,we study the k-nullity distributions and we discuss the isometric immersion of such a manifold M as hypersurface in a real space form M(c) of constant curvature c proving that c is less or equal to −1 and,if c<−1, M is totally umbilical, Kenmotsu and locally isometric to the hyperbolic space of constant curvature −1. Finally, the Einstein and \eta-Einstein conditions are discussed. 2000Mathematics Subject Classification : 53C15; 53C25. Key words and phrases : Almost Kenmotsu manifolds, harmonic morphisms, nullity distributions, real space forms, \eta-Einstein conditions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11586/9245
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