Curvature via the de Sitter’s Space-Time

Authors

  • Graciela María Desideri Dto. de Matem´atica, Universidad Nacional del Sur, Bah´ıa Blanca, Argentina

DOI:

https://doi.org/10.5644/SJM.07.1.09

Keywords:

Central curvature, total central curvature, spherical image, de Sitter's space-time, Lorentzian space

Abstract

We define the central curvature and the total central curvature of a closed curve in a Lorentz $(n + 1)$--space. In addition, we obtain estimates for the total central curvatures of spacelike pure polygons. The study is done by using the n-dimensional de Sitter's space-time.

 

2000 Mathematics Subject Classification. 53B30, 53C50

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References

T. F. Banchoff, Total central curvature of curves, Duke Math. J., (1969), 281–289.

J. K. Been, P. E. Ehrlich and K. L. Easley, Global Lorentzian Geometry, Second Edition, Marcel Dekker, Inc., New York (1996).

G. S. Birman and G. M. Desideri, Projections of pseudosphere in the Lorentz 3-space, Bull. Korean Math. Soc., 44 (3) (2007), 483–492.

G. M. Desideri, On polygons in Lorentzian plane, C. R. Acad. Bulgare Sci., 60 (10) (2007), 1039–1045.

G. M. Desideri, Total central curvature of curves in the 3-dimensional Lorentzian space, Actas del VIII Congreso Monteiro (2005), 39–4

S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-time, Cambridge University Press, London (1976).

J. W. Milnor, On the total curvature of knots, Ann. Math., 52 (2) (1950), 248–257.

B. O’Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press, New York (1983).

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Published

10.06.2024

How to Cite

Desideri, G. M. (2024). Curvature via the de Sitter’s Space-Time. Sarajevo Journal of Mathematics, 7(1), 91–101. https://doi.org/10.5644/SJM.07.1.09

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