Let $(M,g)$ be a Riemannian manifold and let $\lbrace e_1,...,e_n\rbrace$ be a locally frame field on $M$ and $\omega _1 ,...,\omega _n$ be the dual $1$-forms of it. If $\omega _{ij}$ be the connection $1$-forms with respect to the mentioned frame and metric $g$. Then I would like to know what can be the structure equations? I would be grateful if you could give me a link or introduce a book containing these equations.