0000000000850835

AUTHOR

Dirce Kiyomi Hayashida Mochida

showing 2 related works from this author

Inflection points and topology of surfaces in 4-space

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 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.

Surface (mathematics)Applied MathematicsGeneral MathematicsMathematical analysisRegular polygonBullet-nose curveTopologySpace (mathematics)Asymptotic curvesymbols.namesakeInflection pointsymbolsGravitational singularityEuler numberMathematicsTransactions of the American Mathematical Society
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The geometry of surfaces in 4-space from a contact viewpoint

1995

We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.

Computer Science::GraphicsDifferential geometryHyperplaneInflection pointHyperbolic geometryComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)GeometryGeometry and TopologyAlgebraic geometrySpace (mathematics)Topology (chemistry)Projective geometryMathematicsGeometriae Dedicata
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