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From the book: Symplectic Geometry by Ana Cannas da Silva, page 19. The following statement is claimed, but I don't full understand it, neither know how to prove it on my own.

Two functions generate the same lagrangian submanifold if and only if they differ by a locally constant function.

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    It's a lot like saying "two functions have the same derivative if and only if they differ by a constant". (I assume there are already conditions about differentiability of the functions, I don't have the book in front of me to remember which.) Which terms are you most confused about? i.e. do you know how a function generates a lagrangian submanifold?

    E.g. "locally constant" sounds fancy but it really means, constant on each connected component of the manifold they're defined on; usually we have just one connected component and mean a constant function.

     – Elizabeth S. Q. Goodman Mar 28 '17 at 16:17
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    @ElizabethS.Q.Goodman Actually, it was about 'locally constant', thanks Elizabeth. –  Mar 28 '17 at 16:20

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