  A graphene bilayer in a transverse magnetic field has a set of Landau levels
with energies $E=\pm \sqrt{N(N+1)}\hslash \omega_{c}^{\ast}$ where
$\omega_{c}^{\ast}$ is the effective cyclotron frequency and $% N=0,1,2,...$
All Landau levels but N=0 are four times degenerate counting spin and valley
degrees of freedom. The Landau level N=0 has an extra degeneracy due to the
fact that orbitals $n=0$ and $n=1$ both have zero kinetic energies. At integer
filling factors, Coulomb interactions produce a set of broken-symmetry states
with partial or full alignement in space of the valley and orbital pseudospins.
These quantum Hall pseudo-ferromagnetic states support topological charged
excitations in the form of orbital and valley Skyrmions. Away from integer
fillings, these topological excitations can condense to form a rich variety of
Skyrme crystals with interesting properties. We study in this paper different
crystal phases that occur when an electric field is applied between the layers.
We show that orbital Skyrmions, in analogy with spin Skyrmions, have a texture
of electrical dipoles that can be controlled by an in-plane electric field.
Moreover, the modulation of electronic density in the crystalline phases are
experimentally accessible through a measurement of their local density of
states
