On Invariants of m-Vector in Lorentzian Geometry

Year 2016, Volume: 9 Issue: 1, 38 - 44, 30.04.2016

İdris Ören

https://doi.org/10.36890/iejg.591885

Cited By: 3

Abstract

Keywords

Invariant, Lorentz group

References

• [1] Duggal, Krishan L. and Bejancu, A., Lightlike submanifolds of semi-Riemannian manifolds and applications. Kluwer Academic Publishers, Dordrecht, 1996.
• [2] Greub, W., Linear Algebra. Springer-Verlag, 1967.
• [3] Hilbert, D., Theory of algebraic invariants. Cambridge Univ.Press, New York, 1993.
• 4] Höfer,R., m-point invariants of real geometries. Beitrage Algebra Geom. 40(1999), 261-266.
• [5] Khadjiev, D. and Göksal, Y.,Applications of hyperbolic numbers to the invariant theory in two-dimensional pseudo-Euclidean space. Adv.Appl. Clifford Algebras, Online First Article (2015),1-24.
• [6] Misiak, A. and Stasiak, E., Equivariant maps between certain G-spaces with G=O(n-1,1).Mathematica Bohemica 3(2001), 555-560.
• [7] Naber, G. L., The Geometry of Minkowski spacetime: an introduction to the mathematics of the special theory of relativity. Springer- Verlag, New York, 1992.
• [8] Ören, I˙., Invariants of points for the orthogonal group O(3, 1). Doctoral thesis, Karadeniz Technical University, 2008.
• [9] Ören, I˙., Complete system of invariants of subspaces of Lorentzian space. Iran. J. Sci. Technol. Trans. A Sci. (2016),1-22. (in press).
• [10] Ören, I˙., The equivalence problem for vectors in the two-dimensional Minkowski spacetime and its application to Bézier curves. J. Math. Comput. Sci. 6 (2016), no. 1, 1-21.
• [11] Stasiak, E., Scalar concomitants of a system of vectors in pseudo-Euclidean geometry of index 1. Publ.Math..Debrecen 57(2000),no. 1-2, 55-69.
• [12] Study,E., The first main theorem for orthogonal vector invariants. Ber.Sachs. Akad. 136(1897).
• [13] Sturmfels, B.,Algorithms in invariant theory. Springer-Verlag, Wien, 2008.
• [14] Weyl, H., The classical groups:Their invariants and representations. Princeton University Press, Princeton, NJ, 1997.