INFLECTION POINTS AND TOPOLOGY OF SURFACES IN 4-SPACE

@inproceedings{Garca2000INFLECTIONPA,
  title={INFLECTION POINTS AND TOPOLOGY OF SURFACES IN 4-SPACE},
  author={Ram{\'o}n Abascal Garc{\'i}a and DIRCE KIYOMI HAYASHIDA MOCHIDA and Mar{\'i}a del Carmen Romero Fuster and MARIA APARECIDA SOARES RUAS},
  year={2000}
}
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 Poincaré-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… CONTINUE READING

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