 Embedding Condition 1: We must first designate a point as the center of \(\Sigma(M_{p})\) and then require that they coincide or cover the point \(p \in M\). This leads, Weyl says, to a restriction in the choice of a normal coordinate system \(\xi\) on \(\Sigma(M_{p})\). And because \(G\) acts transitively, a normal coordinate system \(\xi\) on \(\Sigma(M_{p})\) can be chosen such that the normal coordinates \(\xi\) vanish at the center, that is, \(\xi^{1} = \xi^{2} = \cdots = 0\). The group \(G\) is therefore restricted to the subgroup \(G_{0}\) of all representations of \(G\) which leave the center invariant. 