Hedgehogs are a natural generalization of convex bodies of class C+ 2. After recalling some basic facts concerning this generalization, we use the notion of index to study differential and integral geometries of hedgehogs.
As applications, we prove a particular case of the Tennis Ball Theorem and a property of normals to a plane convex body of constant width.
@article{urn:eudml:doc:41391, title = {Indice d'un h\'erisson: \'etude et applications.}, journal = {Publicacions Matem\`atiques}, volume = {44}, year = {2000}, pages = {237-255}, mrnumber = {MR1775763}, zbl = {0974.53003}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41391} }
Martínez-Maure, Yves. Indice d'un hérisson: étude et applications.. Publicacions Matemàtiques, Tome 44 (2000) pp. 237-255. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41391/