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.



Reference request for structure equations
This book must be useful: *An Introduction to Differentiable Manifolds and Riemannian Geometry written by William Munger Boothby* Page 319. Read online in [Google Link](https://books.google.com/books?id=DFYs99E-IFYC&pg=PR13&dq=An+Introduction+to+Differentiable+Manifolds+and+Riemannian+Geometry&hl=en&sa=X&ved=0ahUKEwj89_-m9tfPAhVJkSwKHaSMCUYQ6AEIHjAA#v=onepage&q=An%20Introduction%20to%20Differentiable%20Manifolds%20and%20Riemannian%20Geometry&f=false).


