  By breaking both the axial and the spatial reflection symmetries, we develop
multidimensionally constrained relativistic mean field (MDC-RMF) models. The
nuclear shape is assumed to be invariant under the reversion of $x$ and $y$
axes, i.e., the intrinsic symmetry group is $V_{4}$ and all shape degrees of
freedom $\beta_{\lambda\mu}$ with even $\mu$, such as $\beta_{20}$,
$\beta_{22}$, $\beta_{30}$, $\beta_{32}$, $\beta_{40}$, $\dots$, are included
self-consistently. The Dirac wave functions are expanded in an axially deformed
harmonic oscillator basis. The RMF functional can be one of the following four
forms: the meson exchange or point-coupling nucleon interactions combined with
the nonlinear or density-dependent couplings. The pairing effects are taken
into account with the BCS approach. The 1-, 2-, and 3-D potential energy
surfaces (PES's) of $^{240}$Pu are illustrated for numerical checks and for the
study of the effect of the triaxiality on the fission barriers. Potential
energy curves of even-even actinide nuclei around the first and second fission
barriers are studied systematically. Besides the first ones, the second fission
barriers in these nuclei are also lowered considerably by the triaxial
deformation. This lowering effect is independent of the effective interactions
used in the RMF functionals. Further discussions are made about different
predictions on the effect of the triaxiality between the
macroscopic-microscopic and MDC-RMF models, possible discontinuities on PES's
from self-consistent approaches, and the restoration of broken symmetries.
MDC-RMF models give reasonably good description of fission barriers of
even-even actinide nuclei. It is important to include both the nonaxial and the
reflection asymmetric shapes simultaneously for the study of PES's and fission
barriers of actinide nuclei and of those in unknown mass regions such as, e.g.,
superheavy nuclei.
