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- W2783100738 abstract "For every real numbers a⩾1, b⩾1 with (a,b)≠(1,1), the curve parametrized by θ∈R valued in C2≅R4γ:θ⟼(x(θ)+−1y(θ),u(θ)+−1v(θ)) with components:x(θ):=a−1a(ab−1)cosθ,y(θ):=b(a−1)ab−1sinθ,u(θ):=b−1b(ab−1)sinθ,v(θ):=−a(b−1)ab−1cosθ, has image contained in the CR-umbilical locus:γ(R)⊂UmbCR(Ea,b)⊂Ea,b of the ellipsoid Ea,b⊂C2 of equation ax2+y2+bu2+v2=1, where the CR-umbilical locus of a Levi nondegenerate hypersurface M3⊂C2 is the set of points at which the Cartan curvature of M vanishes. Pour tous nombres réels a⩾1, b⩾1 avec (a,b)≠(1,1), la courbe paramétrée par θ∈R à valeurs dans C2≅R4γ:θ⟼(x(θ)+−1y(θ),u(θ)+−1v(θ)) ayant pour composantes :x(θ):=a−1a(ab−1)cosθ,y(θ):=b(a−1)ab−1sinθ,u(θ):=b−1b(ab−1)sinθ,v(θ):=−a(b−1)ab−1cosθ, est d'image contenue dans le lieu CR-ombilic :γ(R)⊂UmbCR(Ea,b)⊂Ea,b de l'ellipsoïde Ea,b⊂C2 d'équation ax2+y2+bu2+v2=1, où le lieu CR-ombilic d'une hypersurface Levi non dégénérée M3⊂C2 est l'ensemble des points en lesquels la courbure de Cartan de M s'annule." @default.
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- W2783100738 date "2018-02-01" @default.
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- W2783100738 title "Parametric CR-umbilical locus of ellipsoids in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mrow><mml:mi mathvariant=double-struck>C</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:math>" @default.
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- W2783100738 doi "https://doi.org/10.1016/j.crma.2017.11.019" @default.
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