engleski

Null scrolls, B-scrolls and associated evolute sets in Lorentz-Minkowski 3-space

In classical differential geometry in Euclidean space, the Bonnet’s theorem states that there are two surfaces of constant mean curvature parallel a surface of constant positive Gaussian curvature. These two constant mean curvature surfaces are so- called harmonic evolutes of each other. In this short presentation, we present results of the analogous investigation in Lorentz- Minkowski 3- space, however, restricted to the case of surfaces that have no Euclidean counterpart, the quasi- umbilical surfaces. These surfaces are characterized by the property that their shape operator is not diagonalizable, and they can be parametrized as null scrolls or B- scrolls.

Null scrolls ; B-scrolls ; evolute sets ; Lorentz-Minkowski 3-space

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