6533b836fe1ef96bd12a1c2f
RESEARCH PRODUCT
Inflection points and topology of surfaces in 4-space
Dirce Kiyomi Hayashida MochidaRonaldo GarciaMaria Del Carmen Romero FusterMaria Aparecida Soares Ruassubject
Surface (mathematics)Applied MathematicsGeneral MathematicsMathematical analysisRegular polygonBullet-nose curveTopologySpace (mathematics)Asymptotic curvesymbols.namesakeInflection pointsymbolsGravitational singularityEuler numberMathematicsdescription
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.
year | journal | country | edition | language |
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2000-03-15 | Transactions of the American Mathematical Society |