## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the flatness of a class of metric f-manifolds

#### Abstract

We consider a metric $f$--structure on a manifold $M$ of dimension $2n+s$. We suppose that its kernel is paralellizable by global orthonormal vector fields $\xi_1,\dots,\xi_s$ and that the dual 1--forms satisfy $d\eta^k=F$ where $F$ is the associated Sasaki 2--form and $k=1,\dots,s$. We prove that if $n$ is greater than one then $M$ cannot be flat. This is a generalization of a result by D.E.Blair proved for contact metric manifolds. We also give a counterexample in the case $n=1$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 3 (2003), 461-474.

Dates
First available in Project Euclid: 12 September 2003

https://projecteuclid.org/euclid.bbms/1063372350

Digital Object Identifier
doi:10.36045/bbms/1063372350

Mathematical Reviews number (MathSciNet)
MR2017456

Zentralblatt MATH identifier
1078.53081

#### Citation

Di Terlizzi, Luigia; Konderak, Jerzy J.; Pastore, Anna Maria. On the flatness of a class of metric f-manifolds. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 3, 461--474. doi:10.36045/bbms/1063372350. https://projecteuclid.org/euclid.bbms/1063372350