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Showing papers by "Maria Aparecida Soares Ruas published in 2000"

Journal Article•DOI•
Inflection points and topology of surfaces in 4-space

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Ronaldo Garcia1, Dirce Kiyomi Hayashida Mochida2, Maria del Carmen Romero Fuster3, Maria Aparecida Soares Ruas4•
Universidade Federal de Goiás1, Federal University of São Carlos2, University of Valencia3, Spanish National Research Council4
15 Mar 2000-Transactions of the American Mathematical Society
TL;DR: In this paper, it was shown that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.
Abstract: We consider asymptotic line fields on generic surfaces in 4-space and show that they are globally defined on locally convex surfaces, and their singularities are the inflection points of the surface. As a consequence of the generalized Poincare-Hopf formula, we obtain some relations between the number of inflection points in a generic surface and its Euler number. In particular, it follows that any 2-sphere, generically embedded as a locally convex surface in 4-space, has at least 4 inflection points.

66 citations