Consider the metric

\[
d s^{2}=\frac{R^{2}}{ho^{2}-R^{2}} d ho^{2}+ho^{2} d \theta^{2}+ho^{2} \sin ^{2} \theta d \phi^{2}
\]

which can be considered to be derived from a "Lorentzian" metric

\[
d s^{2}=d x^{2}+d y^{2}+d z^{2}-d w^{2}
\]

by the three-dimensional restriction

\[
w^{2}=x^{2}+y^{2}+z^{2}-R^{2}=ho^{2}-R^{2} .
\]

Find a parametric expression for the geodesics in terms of the time \(t\).