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

Abstract

In this paper, we study harmonic evolutes of [Formula: see text]-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 [Formula: see text]-scrolls turn out to be curves. In particular, we show that the harmonic evolute of a [Formula: see text]-scroll of constant mean curvature together with its base curve forms a null Bertrand pair. This allows us to characterize [Formula: see text]-scrolls of constant mean curvature and reconstruct them from a given null curve which is their harmonic evolute.

On the Harmonic Evolute Surfaces of Tubular Surfaces in Euclidean 3-Space

“…where   , Hs  and   , Ns  are the mean curvature and the normal vector field of a surface   , Ts  , respectively. Many international studies have been conducted on the harmonic evolute surface of a surface, some of which are [1][2][3][4][5]. In this study, harmonic evolute surface of a tubular surface was investigated in order to give direction to the surfaces of differential geometry, which finds application in multiple disciplines.…”

On the Harmonic Evolute Surfaces of Hasimoto Surfaces

“…Let = ( , ) be a surface and also its normal and denotes its non-zero mean curvature. Then, the harmonic evolute surface of = ( , ) is given by parametrically see for more details, [1][2][3].…”

A Study on the Harmonic Evolute Surfaces of Quasi Binormal Surfaces

“…After it was initially discovered by Gaspard Mongea, many researchers have studied ruled surfaces [1][2][3][4]. Besides ruled surfaces, harmonic evolute surfaces of various surfaces have been also studied [5][6][7][8]. In addition to these studies, we work on the harmonic evolute surfaces of the ruled surfaces generated by quasi binormal vector [9].…”