  On anisotropic lattices with the anisotropy $\xi=a_\sigma/a_\tau$ the
following basic parameters are calculated by perturbative method: (1) the
renormalization of the gauge coupling in spatial and temporal directions,
$g_\sigma$ and $g_\tau$, (2) the $\Lambda$ parameter, (3) the ratio of the
renormalized and bare anisotropy $\eta=\xi/\xi_B$ and (4) the derivatives of
the coupling constants with respect to $\xi$, $\partial g_\sigma^{-2}/\partial
\xi$ and $\partial g_\tau^{-2}/\partial \xi$. We employ the improved gauge
actions which consist of plaquette and six-link rectangular loops, $c_0 P(1
\times 1)_{\mu \nu} + c_1 P(1 \times 2)_{\mu \nu}$. This class of actions
covers Symanzik, Iwasaki and DBW2 actions. The ratio $\eta$ shows an impressive
behavior as a function of $c_{1}$, i.e.,$\eta>1$ for the standard Wilson and
Symanzik actions, while $\eta<1$ for Iwasaki and DBW2 actions. This is
confirmed non-perturbatively by numerical simulations in weak coupling regions.
The derivatives $\partial g^{-2}_{\tau}/\partial \xi$ and $\partial
g^{-2}_{\sigma}/\partial \xi$ also changes sign as $-c_{1}$ increases. For
Iwasaki and DBW2 actions they become opposite sign to those for standard and
Symanzik actions. However, their sum is independent of the type of actions due
to Karsch's sum rule.
