On the flatness of a class of metric f-manifolds
Di Terlizzi, Luigia ; Konderak, Jerzy J. ; Pastore, Anna Maria
Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 461-474 / Harvested from Project Euclid
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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 $n=1$.
Publié le : 2003-09-14
Classification:  metric f-structure,  almost ${\cal S}$--manifold,  flat manifold,  53D10,  70G45 
@article{1063372350,
     author = {Di Terlizzi, Luigia and Konderak, Jerzy J. and Pastore, Anna Maria},
     title = {On the flatness of a class of metric f-manifolds},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 461-474},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1063372350}
}

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, Tome 10 (2003) no. 1, pp.  461-474. http://gdmltest.u-ga.fr/item/1063372350/