Abstract

GIGENA, Salvador. Classificatory problems in affine geometry approached by differential equations methods. Rev. Unión Mat. Argent. [online]. 2006, vol.47, n.2, pp.95-107. ISSN 0041-6932.

We present in this survey article an account of some examples on the use of nonlinear differential equations, both partial and ordinary, that have been applied to the treatment of classificatory problems in affine geometry of hypersurfaces. Locally strongly convex, complete affine hyperspheres is the first topic explained, then hypersurfaces of decomposable type, and, finally, those with parallel second fundamental (cubic) form.

        · text in English     · English ( pdf )