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Caustics and wave front propagations: applications to differential geometry

Shyuichi Izumiya, Masatomo Takahashi (2008)

Banach Center Publications

This is mainly a survey on the theory of caustics and wave front propagations with applications to differential geometry of hypersurfaces in Euclidean space. We give a brief review of the general theory of caustics and wave front propagations, which are well-known now. We also consider a relationship between caustics and wave front propagations which might be new. Moreover, we apply this theory to differential geometry of hypersurfaces, getting new geometric properties.

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