  In recent papers, summarized in survey [1], we construct a number of examples
of non standard lagrangian tori on compact toric varieties and as well on
certain non toric varieties which admit pseudotoric structures. Using this
pseudotoric technique we explain how non standard lagrangian tori of Chekanov
type can be constructed and what is the topological difference between standard
Liouville tori and the non standard ones. However we have not discussed the
natural question about the periods of the constructed twist tori; in particular
the monotonicity problem for the monotonic case was not studied there. In the
paper we present several remarks on these questions, in particular we show for
the monotonic case how to construct non standard lagrangian tori which satisify
the monotonicity condition. First of all we study non standard tori which are
Bohr - Sommerfeld with respect to the anticanonical class. This notion was
introduced in [2], where one defines certain universal Maslov class for the
${\rm BS}_{can}$ lagrangian submanifolds in compact simply connected monotonic
symplectic manifolds. Then we show how monotonic non standard lagrangian tori
of Chekanov type can be constructed. Furthemore we extend the consideration to
pseudotoric setup and construct examples of monotonic lagrangian tori in non
toric monotonic manifolds: complex 4 - dimensional quadric and full flag
variety $F^3$.
