Search results for "Asymptotic curve"

showing 2 items of 2 documents

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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ASYMPTOTIC CURVES ON SURFACES IN ℝ5

2008

We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.

Surface (mathematics)Asymptotic curveAsymptotic analysisApplied MathematicsGeneral MathematicsSecond fundamental formMathematical analysisGravitational singularityAsymptotic expansionMathematicsCommunications in Contemporary Mathematics
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