004对分量的指标升降

$$\begin{gathered} {\xi }^{\alpha }=(\xi ,g^{\alpha }) \\ ={\xi }^{\alpha }=(\xi ,g^{\alpha ,\beta }\ast g_{\beta }) \\ =g^{\alpha ,\beta }\ast (\xi ,g_{\beta }) \\ =g^{\alpha ,\beta }\ast {\xi }_{\beta } \end{gathered}$$

$$\begin{gathered} \{\begin{array}{l}{\xi }^{\alpha }=g^{\alpha ,\beta }\ast {\xi }_{\beta }\\ \\ {\xi }_{\alpha }=g_{\alpha ,\beta }\ast {\xi }^{\beta }\end{array} \\ 这个就是著名的指标升降(是对分量而言的) \end{gathered}$$