This thesis is concerned with exact solutions of Einstein's field equations of general relativity, in particular, when the source of the gravitational field is a perfect fluid with a purely electric Weyl tensor. General relativity, cosmology and computer algebra are discussed briefly. A mathematical introduction to Riemannian geometry and the tetrad formalism is then given. This is followed by a review of some previous results and known solutions concerning purely electric perfect fluids. In addition, some orthonormal and null tetrad equations of the Ricci and Bianchi identities are displayed in a form suitable for investigating these space-times. Conformally flat perfect fluids are characterised by the vanishing of the Weyl tensor and form a sub-class of the purely electric fields in which all solutions are known (Stephani 1967). The number of Killing vectors in these space-times is investigated and results presented for the non-expanding space-times. The existence of stationary fields that may also admit 0, 1 or 3 spacelike Killing vectors is demonstrated. Shear-free fluids in the class under consideration are shown to be either non-expanding or irrotational (Collins 1984) using both orthonormal and null tetrads. A discrepancy between Collins (1984) and Wolf (1986) is resolved by explicitly solving the field equations to prove that the only purely electric, shear-free, geodesic but rotating perfect fluid is the Godel (1949) solution. The irrotational fluids with shear are then studied and solutions due to Szafron (1977) and Allnutt (1982) are characterised. The metric is simplified in several cases where new solutions may be found. The geodesic space-times in this class and all Bianchi type 1 perfect fluid metrics are shown to have a metric expressible in a diagonal form. The position of spherically symmetric and Bianchi type 1 space-times in relation to the general case is also illustrated.

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The thesis considers various problems in general relativity concerning projective and Ricci collineations. A result due to Yano in the maximum dimension of the projective algebra on a non-flat space-time is improved using a pointwise classification scheme. The converse of a result, relating Weyl projective vector fields and curvature collineations under certain well defined circumstances, is given. A result is presented showing that, under specified conditions a space-time admitting a proper special projective vector field admits a proper special conformal vector field and vice versa. The work done on Ricci/Matter collineations gives a general mathematical treatment of these vector fields where particular emphasis is placed on decomposable space-times. Problems of differentiability, extendibility, etc are described.

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This thesis investigates the possibilities and parameters of intersensory substitution - the provision through one sense of information normally provided through another sense. An artificial ultrasonic echo-location device, providing, through sound, information usually provided through sight, was used. A series of interlinked cross-sectional and longitudinal studies was run, using both blind and simulated blind subjects of a range of ages. Infants, pre-school children, school-age children and adults were tested. Although some subjects in all age groups were shown to be able to make some use of the device, by adopting strict criteria for testing the effectiveness of this use, both qualitative and quantitative age differences in use were demonstrated to exist. The implications of these results for conflicting theories of development, in particular perceptual development, are considered. A differentiation theory in which development is seen as proceeding from abstract to specific, while not consistent with all the results, is shown with modification, to have the greatest explanatory value.

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The aim of this thesis is to study certain linear connections arising in physics; and in particular metric connections, Weyl connections and Cartan connections are examined. Emphasis is placed on the holonomy group of the connection and the relationships between the relevant geometric objects in the physical theories. The appropriate mathematical background is reviewed in the first two chapters and various notions from differential geometry are introduced. Proofs of theorems relating covariantly constant and recurrent tensors with holonomy are given in detail, and Eisenhart's results on connections induced in submanifolds are given a modern treatment. The relationship between a metric, its Levi-Civita connection and its curvature tensor is examined in chapter three. Some new results on the problem of how to 'recognise' a metric curvature are presented and the idea of a 'curvature copy' - different linear connections with the same curvature - is discussed. Weyl's elegant attempt to unify gravity with electromagnetism is the topic of the fourth chapter. A full holonomy classification of Weyl connections is given in this chapter, along with results concerning the relationship between metric, connection and curvature. The Cartan connection was introduced by Cartan as a device for placing Newtonian gravity in a similar formal setting to Einstein's theory of gravity. This connection is studied in chapter five and reference is made to holonomy properties, symmetries and reduction of the bundle - which enables Newtonian gravity to take on the appearance of a gauge field theory.

The purpose of this thesis is to present some new ideas related to the classification of second order symmetric tensors in general relativity theory. In the introductory chapter, the tensors which are to be classified are defined and their role in Einstein's theory discussed. An introduction to tetrads, null rotations and the theory of bivectors as well as a summary of some of the main contributions to classification theory and its applications are also provided in the first chapter. The second chapter contains brief descriptions of the known methods of classifying the Weyl and Ricci tensors. In addition, new methods of classifying the E tensor and of classifying bivectors by Segre type are discussed. The contribution due to the E tensor when a spherically symmetric cloud of test particles is scattered by a gravitational field is analysed, thus extending some known results. As an example of the classification of second order tensors, the Segre type of the energy-momentum tensor for a moving charged particle is calculated. Chapter Three is concerned with spaces admitting symmetries and in particular the restrictions imposed on the Ricci tensor by locally isotropic space-times. A short proof is presented of a known result concerning a symmetry in an Einstein-Maxwell space-time. The classifications of the Ricci tensor due to Ludwig and Scanlon and Penrose are investigated in the final chapter. The correspondence between these schemes and the Segre classification is examined using an entirely vector approach. The projective model constructed by Penrose is discussed in detail and some ideas pertaining to this model are extended.

The purpose of this thesis is to study in depth the relationship between the curvature of space-time and the other geometrical objects which naturally arise in general relativity. Most of the results obtained apply to the generic case. Chapter 1 contains a discussion of certain aspects of fibre bundle theory required in later chapters which may be unfamiliar to many relativists, while chapter 2 contains preliminary material on curvature in relativity and proves a continuity property of the algebraic classification of the Weyl and energy-momentum tensors. Chapter 3 describes the generic behaviour of the Riemann, Weyl and energy-momentum tensors, and chapter 5 goes on to use this description to investigate the relationship of the Riemann tensor to the metric, conformal class and connection of space-time in the generic case. In particular it is proved that the Riemann tensor uniquely and continuously determines the connections. The information obtained in chapter 3 on the algebraic type of curvature in the general case is related in chapter 4 to the topology of the underlying manifold. In chapter 6 a topology is defined on the set of sectional curvatures of all Lorentz metrics on a given manifold. The remainder of the chapter attempts to do for the sectional curvature what was done for the Riemann tensor in chapter 5 but, because sectional curvature is more difficult to handle, the results obtained are necessarily more modest.