Open Access
Translator Disclaimer
September 2003 On the flatness of a class of metric f-manifolds
Luigia Di Terlizzi, Jerzy J. Konderak, Anna Maria Pastore
Bull. Belg. Math. Soc. Simon Stevin 10(3): 461-474 (September 2003). DOI: 10.36045/bbms/1063372350

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 $n=1$.

Citation

Download Citation

Luigia Di Terlizzi. Jerzy J. Konderak. Anna Maria Pastore. "On the flatness of a class of metric f-manifolds." Bull. Belg. Math. Soc. Simon Stevin 10 (3) 461 - 474, September 2003. https://doi.org/10.36045/bbms/1063372350

Information

Published: September 2003
First available in Project Euclid: 12 September 2003

zbMATH: 1078.53081
MathSciNet: MR2017456
Digital Object Identifier: 10.36045/bbms/1063372350

Subjects:
Primary: 53D10, 70G45

Rights: Copyright © 2003 The Belgian Mathematical Society

JOURNAL ARTICLE
14 PAGES


SHARE
Vol.10 • No. 3 • September 2003
Back to Top