In the dissertation Estabilidade Estrutural de Primeira Ordem e Variedades de Banach ("First order structural stability and Banach manifolds") he presented a geometric reinterpretation and extension of the fruitful notions and results relating bifurcations and stability that were introduced by A.
[2] He also was a Fellow of John Simon Guggenheim Memorial Foundation[permanent dead link] (1983).
He is also author of the books Lines of Curvature and Umbilical Points on Surfaces, 18o CBM, Publicações Matemáticas, IMPA,(1991) with Carlos Gutierrez, reprinted and updated as Structurally Configurations of Lines of Curvature and Umbilic Points on Surfaces, Lima, Monografias del IMCA, (1998) and Differential Equations of Classical Differential Geometry, a Qualitative Theory, 27o CBM, Publicações Matemáticas, IMPA, (2009) with Ronaldo Garcia.
Introduced, with Carlos Gutierrez, the concept of "principal configuration" of curvature lines on surfaces.
See Structurally Stable Configurations of Lines of Principal Curvature", Astérisque, França, v. 98–99, p. 195–215, (1982).