On the Second Kind Twisted Surfaces in Minkowski 3-Space

Abstract

In this paper, we introduce the notion of the second kind twisted surfaces in Minkowski 3-space. We classify all non-degenerate second kind twisted surfaces in terms of flat, minimal, constant Gaussian and constant mean curvature surfaces, with respect to a chosen lightlike transversal bundle. We also prove that a lightlike second kind twisted surfaces, with respect to a chosen lightlike transversal vector bundle, are the lightcones, the lightlike binormal surfaces over pseudo null base curve and the lightlike ruled surfaces with null rulings whose base curve lies on lightcone.

Flat double rotational surfaces in Euclidean and Lorentz-Minkowski 4-space

“…Indeed, as is clear from e.g. [4,6], including profile curves in lightlike planes and performing rotations about lightlike axes lead to necessary adjustments of the construction of twisted surfaces and to substantially different results. Hence, in this work only profile curves in non-null planes and rotations keeping invariant non-null planes are taken into account.…”

“…Together with Van de Woestyne the author studied another generalization of rotational surfaces, namely, twisted surfaces, see [4] and the references therein. Later, a second kind of twisted surfaces was defined in [6]. Twisted surfaces were first defined in [5] and are constructed by rotating a planar curve about an axis in its supporting plane while simultaneously rotating it in its supporting plane.…”

Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$

“…The notion of the second kind twisted surfaces in Minkowski 3-space was introduced by Grbović et al [8]. They classified all non-degenerate second kind twisted surfaces in terms of flat, minimal, constant Gaussian and constant mean curvature surfaces, with respect to a chosen lightlike transversal bundle.…”

Twisted surfaces with vanishing curvature in Galilean 3-space

“…Van de Woestyne, defined twisted surfaces in Minkowski 3-space and classified those with constant Gaussian curvature or constant mean curvature, see [7,8,9]. Later, in [11], a second type of twisted surfaces in Minkowski 3-space is considered by other authors. In this article, we define three types of twisted surfaces in Galilean 3-space.…”