(1) Instituto de Matemática Pura e Aplicada—IMPA, Estrada Dona Castorina 110—Horto, 22460-320 Rio de Janeiro, RJ, BRAZIL
Abstract:
We construct, for any good Cantor set F of Sn-1, an immersion of the sphere Sn with set of points of zero Gauss-Kronecker curvature equal to F × D1, where D1 is the 1-dimensional disk. In particular these examples show that the theorem of Matheus-Oliveira strictly extends two results by do Carmo-Elbert and Barbosa-Fukuoka-Mercuri.To professor João Lucas Barbosa, in occasion of his 60th birthday. Supported by CNPq/Brazil. Supported by Faperj/Brazil.