# What is a Lagrangian submanifold?

I see references to Lagrangian Submanifolds in the literature but don't know what they are. Is there a relation to Lagrangian Tori (which I also don't know what are). Could someone give a definition that includes an intuitive explanation for what their use is?

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It's not entirely clear from your question whether you found these definitions: en.wikipedia.org/wiki/… and planetmath.org/encyclopedia/LagrangianSubmanifold.html . –  joriki Apr 11 '11 at 5:53