Genericity of Caustics and Wavefronts on an r-corner

We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold. We also give simpler proofs of main results in T. Tsukada, "Reticular Lagrangian Singularities," Asian J. Math., 1 (1997), pp. 572-622 and T. Tsukada, "Reticular Legendrian Singularities," Asian J. Math., 5:1 (2001), pp. 109-127.

Keywords

Caustic, wavefront, r-corner, stability, genericity

2010 Mathematics Subject Classification

53Dxx, 58K25

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Published 1 January 2010