Hypersurfaces that are not null

Can space-like or time-like hypersurfaces defined by $\displaystyle n^{\alpha}n_{\alpha} = \varepsilon \equiv \cases{-1\ \sum \ (\text{space-like case}) \\ \\ +1\ \sum \ (\text{time-like case})} \hspace{3cm} \small \text{where} \ n_{\alpha} = \frac{\varepsilon \Phi_{\alpha}}{\vert \text{g}^{\mu v} \Phi_{\mu} \Phi_v \vert^{\frac{1}{2}}}$

have geodesics that also contain an affine parameter $\lambda$ ?

#Geometry

Easy Math Editor

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$