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Question Number 197344 by MathedUp last updated on 14/Sep/23

$$\frac{\mathrm{d}}{\mathrm{d}t}\cdot \frac{\mathrm{d}{x}^{\mathit{\lambda }}}{\mathrm{d}t}+\frac{1}{2}{\mathrm{g}}^{\mathit{\lambda }\mathit{\alpha }}({\partial }_{\mathit{\mu }}^{}{\mathrm{g}}_{\mathit{\alpha }\mathit{\nu }}+{\partial }_{\mathit{\nu }}^{}{\mathrm{g}}_{\mathit{\alpha }\mathit{\mu }}-{\partial }_{\mathit{\alpha }}^{}{\mathrm{g}}_{\mathit{\mu }\mathit{\nu }})\frac{\mathrm{d}{x}^{\mathit{\mu }}}{\mathrm{d}t}\cdot \frac{\mathrm{d}{x}^{\mathit{\nu }}}{\mathrm{d}t}=0$$

Commented by TheHoneyCat last updated on 20/Sep/23

I'm guessing you're looking for a paramedic expression of a geodesic, but if you don't give us the metric, we can't really do much.

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