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The Euler theorem and Dupin indicatrix for surfaces at a constant distance from edge of regression on a surface in \(E_1^3\). (English) Zbl 1313.53082

The authors consider a surface \(M^f\) at a constant distance from the edge of regression on a surface \(M\) in the Minkowski \(3\)-space \(E^3_1\). Using the notions of hyperbolic angle and normal curvature, they give the Euler theorem for the surface \(M^f\) in \(E^3_1\). They show that the Dupin indicatrix of \(M^f\) can be an ellipse, two conjugate hyperbolas, or two parallel lines.

MSC:

53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53B30 Local differential geometry of Lorentz metrics, indefinite metrics

Keywords:

Euler theorem
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