Projections of pseudosphere in the Lorentz 3-space
Bull. Korean Math. Soc. 2007 Vol. 44, No. 3, 483-492
Printed September 1, 2007
Graciela S. Birman and Graciela M. Desideri
Unicen University, Unicen University
Abstract : 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
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