  In this paper we study how to attack, through different techniques, a perfect
fluid Bianchi I model with variable G,c and Lambda, but taking into account the
effects of a $c$-variable into the curvature tensor. We study the model under
the assumption,div(T)=0. These tactics are: Lie groups method (LM), imposing a
particular symmetry, self-similarity (SS), matter collineations (MC) and
kinematical self-similarity (KSS). We compare both tactics since they are quite
similar (symmetry principles). We arrive to the conclusion that the LM is too
restrictive and brings us to get only the flat FRW solution. The SS, MC and KSS
approaches bring us to obtain all the quantities depending on \int c(t)dt.
Therefore, in order to study their behavior we impose some physical
restrictions like for example the condition q<0 (accelerating universe). In
this way we find that $c$ is a growing time function and Lambda is a decreasing
time function whose sing depends on the equation of state, w, while the
exponents of the scale factor must satisfy the conditions
$\sum_{i=1}^{3}\alpha_{i}=1$ and $\sum_{i=1}^{3}\alpha_{i}^{2}<1,$
$\forall\omega$, i.e. for all equation of state$,$ relaxing in this way the
Kasner conditions. The behavior of $G$ depends on two parameters, the equation
of state $\omega$ and $\epsilon,$ a parameter that controls the behavior of
$c(t),$ therefore $G$ may be growing or decreasing.We also show that through
the Lie method, there is no difference between to study the field equations
under the assumption of a $c-$var affecting to the curvature tensor which the
other one where it is not considered such effects.Nevertheless, it is essential
to consider such effects in the cases studied under the SS, MC, and KSS
hypotheses.
