Abstract
Many problems in singularity theory (for instance, the classifications of singularities of caustics and of wavefronts and also of determining the singularities in optimization and variational calculus problems) are understandable only in terms of the geometries of symplectic and contact manifolds. These geometries are pleasantly different from the three usual ones (those of Euclid, Lobachevskii and Riemann).
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A Lagrangian equivalence of two Lagrangian singularities is a mapping from one Lagrangian fibration space to another which maps fibres onto fibres, the first symplectic structure onto the second and the first Lagrangian submanifold onto the second.
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© 1984 Springer-Verlag Berlin Heidelberg
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Arnold, V.I. (1984). Symplectic and Contact Geometries. In: Catastrophe Theory. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96799-3_14
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DOI: https://doi.org/10.1007/978-3-642-96799-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12859-5
Online ISBN: 978-3-642-96799-3
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