Some notes on the differential geometry of linear coframe bundle of a Riemannian manifold

Abstract

In this paper, we construct $f-$structures $F_{\alpha },1 \le \alpha \le {n}$, $\tilde F$ and $\bar F$ on the linear coframe bundle $F^{*}(M)$ of the Riemannian manifold $M$. It is proved that these structures are adapted with the diagonal lift $^{D}g$ of the Riemannian metric $g$ of the manifold $M$ into the linear coframe bundle $F^{*}(M)$. Also we study the integrability and parallelism of the $f-$structures $F_{\alpha },1 \le \alpha \le {n}$, $\tilde F$ and $\bar F$.