  We study the formation of quasi-one- (quasi-1D) and quasi-two-dimensional
(quasi-2D) symbiotic solitons bound by an interspecies dipolar interaction in a
binary dipolar Bose-Einstein condensate. These binary solitons have a repulsive
intraspecies contact interaction stronger than the intraspecies dipolar
interaction, so that they can not be bound in isolation in the absence of an
interspecies dipolar interaction. These symbiotic solitons are bound in the
presence of an interspecies dipolar interaction and zero interspecies contact
interaction. The quasi-1D solitons are free to move along the polarization $z$
direction of the dipolar atoms, whereas the quasi-2D solitons move in the
$x$-$z$ plane. To illustrate these, we consider a $^{164}$Er-$^{166}$Er mixture
with scattering lengths $a$($^{164}$Er)$ =81a_0$ and $a$($^{166}$Er)$ =68a_0$
and with dipolar lengths $a_{\mathrm{dd}}$($^{164}$Er)$\approx
a_{\mathrm{dd}}$($^{166}$Er)$\approx 65a_0$, where $a_0$ is the Bohr radius. In
each of the two components $a> a_{\mathrm{dd}}$, which stops the binding of
solitons in each component in isolation, whereas a binary quasi-1D or a
quasi-2D $^{164}$Er-$^{166}$Er soliton is bound in the presence of an
interspecies dipolar interaction. The stationary states were obtained by
imaginary-time propagation of the underlying mean-field model; dynamical
stability of the solitons was established by real-time propagation over a long
period of time.
