Skew-symmetric matrices and integral curves in Lorentzian spaces
Keywords:
Flow lines, integral curve, linear vector field, Lorentzian space, skew-symmetric matrix.Abstract
We provide some existence results about integral curves of a linear vector field on 3-dimensional Lorentzian space E₁³. Moreover, we have a classification of integral curves ( or flow lines ) of a linear vector field and the normal forms of the matrix corresponding to a mapping A in Lorentzian spaces E₁³ and E₁²ⁿ⁺¹.References
Acratalishian, A. (1989). On the linear vector field in E ,
communications, Faculty of Sciences, University of Ankara, Series A1:
Mathematics and Statistics, 39:21−35.
Duggal, K.L. & Bejancu A. (1996). Lightlike submanifolds of semi
Rie-mannian manifolds and applications, Kluwer Academic Publishers,
The Nedherlands, 303 pp.
Galbis, A. & Maestre, M. (2012). Vector analysis versus vector
calculus, Springer, London, 375 pp.
Hawking, S.W. & Ellis, G.F.R. (1973). The large scale structure of
space-time, Cambridge University Press, New York, 391 pp.
Karger, A. & Novak, J. (1978). Space kinematics and Lie groups,
Gordon and Breach Science Publishers, 422 pp.
Lang, S. (1972). Differential manifolds, Addison-Wesley Publishing
Co., London, 228 pp.
O’Neill, B. (1983). Semi-riemann geometry: with Applications to
Relativity. Academic Pres, New York, 469 pp.
Yaylacı, T. (2006). Linear vector fields and applications, MSc thesis,
Ankara University, The Institute of Science, Ankara, 49 pp.
Yücesan, A., öken A.C., Ayyıldız, N. & Manning, G.S. (2004). On
the relaxed elastic line on Pseudo-hypersurfaces in Pseudo-euclidean
spaces, Applied Mathematics and Computation (AMC), 155(2):353 −
