6533b836fe1ef96bd12a1c2f

RESEARCH PRODUCT

Inflection points and topology of surfaces in 4-space

Dirce Kiyomi Hayashida MochidaRonaldo GarciaMaria Del Carmen Romero FusterMaria Aparecida Soares Ruas

subject

Surface (mathematics)Applied MathematicsGeneral MathematicsMathematical analysisRegular polygonBullet-nose curveTopologySpace (mathematics)Asymptotic curvesymbols.namesakeInflection pointsymbolsGravitational singularityEuler numberMathematics

description

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.

https://doi.org/10.1090/s0002-9947-00-02404-1