Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study the map projections from pseudosphere $S_{1}^{2}$ onto the non-lightlike surfaces in the 3-dimensional Lorentzian space, $% L^{3},$ with curvature zero. We show geometrical means and properties of $% \mathbb{R}\times S_{1}^{1}-$cylindrical, $S^{1}\times L-$cylindrical and $% \mathbb{R}\times H_{0}^{1}-$cylindrical projections defined on $S_{1}^{2}$ to cylinders $\mathbb{R}\times S_{1}^{1},$ $S^{1}\times L$ and $\mathbb{R}% \times H_{0}^{1}$, respectively, and orthographic and stereographic projections on $S_{1}^{2}$ to Lorentzian plane, $L^{2}$.

Keywords: cylindrical projection, stereographic projections, orthographic projection, Lorentzian space, Lorentzian geometry

MSC numbers: 53B30, 53C50