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Isotropic submanifold

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A term used in symplectic and contact geometry. In the case of a symplectic manifold , where is a closed, non-degenerate -form, it denotes a submanifold of such that restricts to zero on the tangent bundle of . In the case of a contact manifold , where locally with a -form satisfying , it refers to a submanifold which is everywhere tangent to . In either case an isotropic submanifold is of dimension at most . An isotropic submanifold of maximal dimension is called a Lagrange submanifold in the former case, and a Legendre submanifold in the latter.

References

[a1] V.I. Arnold, A.B. Givental, "Symplectic geometry" V.I. Arnold (ed.) S.P. Novikov (ed.) , Dynamical Systems IV , Encycl. Math. Sci. , 4 , Springer (1990)
How to Cite This Entry:
Isotropic submanifold. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Isotropic_submanifold&oldid=50362
This article was adapted from an original article by H. Geiges (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article