PROJECTIONS OF PSEUDOSPHERE IN THE LORENTZ 3-SPACE

Birman, Graciela S.; Desideri, Graciela M.

doi:10.4134/BKMS.2007.44.3.483

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PROJECTIONS OF PSEUDOSPHERE IN THE LORENTZ 3-SPACE

Journal title : Bulletin of the Korean Mathematical Society
Volume 44, Issue 3, 2007, pp.483-492
Publisher : The Korean Mathematical Society
DOI : 10.4134/BKMS.2007.44.3.483

Title & Authors

PROJECTIONS OF PSEUDOSPHERE IN THE LORENTZ 3-SPACE
Birman, Graciela S.; Desideri, Graciela M.;

Abstract

In this paper, we study the map projections from pseudo-sphere ${$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;

Language

English

Cited by

References

G. S. Birman and G. M. Desideri, Laplacian on mean curvature vector fields for some non-lightlike surfaces in the 3-dimensional Lorentzian space, Proceedings of the Seventh 'Dr. Antonio A. R. Monteiro' Congress of Mathematics (Spanish), 27-33, Univ. Nac. del Sur, Bahia Blanca, 2003

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B. O`Neill, Semi-Riemannian geometry, With applications to relativity. Pure and Applied Mathematics, 103. Academic Press, Inc., New York, 1983

D. J. Struik, Lectures on Classical Differential Geometry, second edition, Dover Publica- tions, Inc., New York, 1961