Spacelike Loxodromes on Helicoidal Surfaces in Lorentzian n--Space

Timelike Loxodromes on Lorentzian Helicoidal Surfaces in Minkowski n--Space

In this paper, we examine timelike loxodromes on three kinds of Lorentzian helicoidal surfaces in Minkowski $n$--space. First, we obtain the first order ordinary differential equations which determine timelike loxodromes on the Lorentzian helicoidal surfaces in $\mathbb{E}^n_1$ according to the causal characters of their meridian curves. Then, by finding general solutions, we get the explicit parametrizations of such timelike loxodromes. In particular, we investigate the timelike loxodromes on the three kinds of Lorentzian right helicoidal surfaces in $\mathbb{E}^n_1$. Finally, we give an exam…

伪迷向空间中旋转曲面上的恒向线与测地线

Loxodromes and geodesics on rotational surfaces in pseudo-isotropic space

本文首次研究了伪迷向空间 I_p^3 中的恒向线，定义了伪迷向角，并推导出旋转曲面上类空与类时恒向线及测地线的方程。

Bour's Theorem of Spacelike Surfaces in Minkowski 4--Space

In this paper, we study on three kinds of spacelike helicoidal surfaces in Minkowski $4$--space. First, we give an isometry between such helicoidal surfaces and rotational surfaces which is a kind of generalization of Bour theorem in Minkowski $3$--space to Minkowski $4$--space. Then, we investigate geometric properties for such isometric surfaces having same Gauss map. By using these results, we give the parametrizations of isometric pair of surfaces. As a particular case, we examine the right helicoidal surfaces in view of Bour's theorem. Also, we present some examples by choosing the compon…

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

In this work we find all helicoidal surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is $0$ or $1$ and that the surface is ruled. If the generating curve is a Lorentzian circle, we show that the only possibility is that the axis is spacelike and the center of the circle lies in the axis.

Application of a unified Kenmotsu-type formula for surfaces in Euclidean or Lorentzian three-space

Kenmotsu's formula describes surfaces in Euclidean 3-space by their mean curvature functions and Gauss maps. In Lorentzian 3-space, Akutagawa-Nishikawa's formula and Magid's formula are Kenmotsu-type formulas for spacelike surfaces and for timelike surfaces, respectively. We apply them to a few problems concerning rotational or helicoidal surfaces with constant mean curvature. Before that, we show that the three formulas above can be written in a unified single equation.