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    Öğe
    Curvature and Weyl collineations of Bianchi type V spacetimes
    (Elsevier Science Bv, 2009) Camci, U.; Hussain, I.; Kucukakca, Y.
    The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type V spacetimes are studied using rank argument of curvature matrix. It is found that the rank of the 6 x 6 curvature matrix is 3, 4, 5 or 6 for these spacetimes. In one of the rank 3 cases the Bianchi type V spacetime admits proper curvature collineations which form infinite dimensional Lie algebra. (b) Then the Weyl collineations of the Bianchi type V spacetimes are investigated using rank argument of the Weyl matrix. It is obtained that the rank of the 6 x 6 Weyl matrix for Bianchi type V spacetimes is 0, 4 or 6. It is further shown that these spacetimes do not admit proper Weyl collineations, except in the trivial rank 0 case, which obviously form infinite dimensional Lie algebra. In some special cases it is found that these spacetimes admit Weyl collineations in addition to the Killing vectors, which are in fact proper conformal Killing vectors. The obtained conformal Killing vectors form four-dimensional Lie algebra. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.
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    Öğe
    Dirac constraint analysis and symplectic structure of anti-self-dual Yang-Mills equations
    (Indian Academy Sciences, 2006) Camci, U.; Can, Z.; Nutku, Y.; Sucu, Y.; Yazici, D.
    We present the explicit form of the symplectic structure of anti-self-dual Yang-Mills (ASDYM) equations in Yang's J- and K-gauges in order to establish the bi-Hamiltonian structure of this completely integrable system. Dirac's theory of constraints is applied to the degenerate Lagrangians that yield the ASDYM equations. The constraints axe second class as in the case of all completely integrable systems which stands in sharp contrast to the situation in full Yang-Mills theory. We construct the Dirac brackets and the symplectic 2-forms for both J- and K-gauges. The covariant symplectic structure of ASDYM equations is obtained using the Witten-Zuckerman formalism. We show that the appropriate component of the Witten-Zuckerman closed and conserved 2-form vector density reduces to the symplectic 2-form obtained from Dirac's theory. Finally, we present the Backlund transformation between the J- and K-gauges in order to apply Magri's theorem to the respective two Hamiltonian structures.
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    Öğe
    Matter collineation classification of Bianchi type II spacetime
    (Springer/Plenum Publishers, 2006) Camci, U.; Sahin, E.
    In this paper we classified the matter collineations (MCs) of Bianchi type II spacetime according to the degenerate and non-degenerate energy-momentum tensor. It is shown that when the energy-momentum tensor is degenerate, most of the cases yield infinite dimensional MCs whereas some cases give finite dimensional Lie algebras in which there are three, four or five MCs. For the non-degenerate matter tensor cases we obtained that the Lie algebra of MCs is finite dimensional, in which the number of MCs are also three, four or five. Furthermore, we discussed the physical implications of the obtained MCs in the case of perfect fluid as source.