## Bulletin of the Belgian Mathematical Society - Simon Stevin

### 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 isometrical immersion of such a manifold $M$ as hypersurface in a real space form $\widetilde{M}(c)$ of constant curvature $c$ proving that $c \leq -1$ 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.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 4 (2011), 655-666.

Dates
First available in Project Euclid: 8 November 2011

https://projecteuclid.org/euclid.bbms/1320763128

Digital Object Identifier
doi:10.36045/bbms/1320763128

Mathematical Reviews number (MathSciNet)
MR2907610

Zentralblatt MATH identifier
1237.53031

#### Citation

Pastore, Anna Maria; Saltarelli, Vincenzo. Almost Kenmotsu manifolds with conformal Reeb foliation. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 4, 655--666. doi:10.36045/bbms/1320763128. https://projecteuclid.org/euclid.bbms/1320763128