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?
What is a Lagrangian submanifold?
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$\begingroup$
algebraic-topology
manifolds
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1It's not entirely clear from your question whether you found these definitions: http://en.wikipedia.org/wiki/Symplectic_manifold#Lagrangian_and_other_submanifolds and http://planetmath.org/encyclopedia/LagrangianSubmanifold.html . – 2011-04-11
1 Answers
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It's a special kind of submanifold of a symplectic manifold; see the definition on Wikipedia. There was a question about this on Math Overflow not long ago, where you will find some good answers.
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0Since again you posted this answer 2 minutes after I posted a comment, let me explain :-). At first I posted it as an answer (with our discussion about comments and answers in mind), but then I realized that the question asked for a lot more than what I wrote, and in fact could be interpreted such that it doesn't actually ask for a raw definition, so I decided to turn it into a comment instead. – 2011-04-11
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0@joriki: Hello again! No need to apologize. Writing that explanation must have been more work for you than writing the comment in the first place. ;) – 2011-04-11