engleski

Harmonic evolutes of B-scrolls with constant mean curvature in Lorentz–Minkowski space

In this paper, we study harmonic evolutes of B- scrolls, that is, of ruled surfaces in Lorentz– Minkowski space having no Euclidean counterparts. Contrary to Euclidean space where harmonic evolutes of surfaces are surfaces again, harmonic evolutes of B-scrolls turn out to be curves. In particular, we show that the harmonic evolute of a B-scroll of constant mean curvature together with its base curve forms a null Bertrand pair. This allows us to characterize B-scrolls of constant mean curvature and reconstruct them from a given null curve which is their harmonic evolute.

Lorentz–Minkowski space ; harmonic evolute ; B-scroll ; mean curvature

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