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

Monotonic lagrangian tori of standard and non standard types in toric and pseudotoric manifolds