  We investigate geodesic orbits and manifolds for metrics associated with
Schwarzschild geometry, considering space and time curvatures separately. For
`a-temporal' space, we solve a central geodesic orbit equation in terms of
elliptic integrals. The intrinsic geometry of a two-sided equatorial plane
corresponds to that of a full Flamm's paraboloid. Two kinds of geodesics
emerge. Both kinds may or may not encircle the hole region any number of times,
crossing themselves correspondingly. Regular geodesics reach a periastron
greater than the $r_S$ Schwarzschild radius, thus remaining confined to a half
of Flamm's paraboloid. Singular or $s$-geodesics tangentially reach the $r_S$
circle. These $s$-geodesics must then be regarded as funneling through the
`belt' of the full Flamm's paraboloid. Infinitely many geodesics can possibly
be drawn between any two points, but they must be of specific regular or
singular types. A precise classification can be made in terms of impact
parameters. Geodesic structure and completeness is conveyed by
computer-generated figures depicting either Schwarzschild equatorial plane or
Flamm's paraboloid. For the `curved-time' metric, devoid of any spatial
curvature, geodesic orbits have the same apsides as in Schwarzschild
space-time. We focus on null geodesics in particular. For the limit of light
grazing the sun, asymptotic `spatial bending' and `time bending' become
essentially equal, adding up to the total light deflection of 1.75 arc-seconds
predicted by general relativity. However, for a much closer approach of the
periastron to $r_S$, `time bending' largely exceeds `spatial bending' of light,
while their sum remains substantially below that of Schwarzschild space-time.
