Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The vierbein or tetrad theory much used in theoretical physics is a special case of the application of Cartan connection in four-dimensional manifolds. It applies to metrics of any signature. This section is an approach to tetrads, but written in general terms. In dimensions other than 4, words like triad, pentad, funfbein, elfbein etc. have been used. Vielbein covers all dimensions. (In German, vier stands for four and viel stands for many.) If you are looking for a basis-dependent index notation, see tetrad (index notation).

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