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We define $S_a^{lm} = \Big( - \frac{1}{\sin \theta} Y^{lm}_{,\varphi}, \sin \theta\ Y^{lm}_{,\theta} \Big)$ $Y_a^{lm} = \Big( Y^{lm}_{,\theta}, Y^{lm}_{,\varphi} \Big)$ to be the axial vector ...

What does it mean, from the geometrical point of view, use (in General Relativity) of the constraints on the metric tensor's coefficients such that $\Delta g_{ij}=0$? (where $\Delta$ is the Beltrami-...