We consider various constructions of monotone Lagrangian submanifolds of
,
, and quadric
hypersurfaces of
.
In
and
we show that several different known constructions of exotic monotone tori yield
results that are Hamiltonian isotopic to each other, in particular answering a
question of Wu by showing that the monotone fiber of a toric degeneration model of
is Hamiltonian
isotopic to the Chekanov torus. Generalizing our constructions to higher dimensions
leads us to consider monotone Lagrangian submanifolds (typically not tori) of quadrics
and of
which can be understood either in terms of the geodesic flow on
or
in terms of the Biran circle bundle construction. Unlike previously known
monotone Lagrangian submanifolds of closed simply connected symplectic
manifolds, many of our higher-dimensional Lagrangian submanifolds are provably
displaceable.
