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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-9, author = {Shyuichi Izumiya and Masatomo Takahashi}, title = {Caustics and wave front propagations: applications to differential geometry}, journal = {Banach Center Publications}, volume = {83}, year = {2008}, pages = {125-142}, zbl = {1156.57025}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-9} }
Shyuichi Izumiya; Masatomo Takahashi. Caustics and wave front propagations: applications to differential geometry. Banach Center Publications, Tome 83 (2008) pp. 125-142. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc82-0-9/