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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5930-5944 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general discussion of affine vector fields (collineations) in space–time is given following a previous article by Hall and da Costa. Some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established. Some preliminary results regarding homothetic symmetries in two- and three-dimensional space–times are also given. The impossibility of reducing an affine algebra containing proper affine vector fields to homothetic or Killing vector fields, by means of a change of compatible metric, is demonstrated.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 5897-5899 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Some recent results of Beem and Parker regarding tidal accelerations and the algebraic structure of the Riemann tensor are generalized.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2848-2853 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Although curvature collineations (curvature preserving transformations) have been studied within the context of general relativity for 20 years, there has been little attempt to study them systematically and there does not appear to have been a detailed mathematical investigation of their properties. This is the first of two papers that are intended as a contribution to this deficiency. This paper presents a discussion of the more general mathematical aspects of curvature collineations and suggests a program for studying them. The implementation of this program and the analysis of specific examples will be carried out in the second paper.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 2854-2862 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper is the second of a set of two papers on curvature collineations in general relativity. The first paper presented the mathematical basis of curvature collineations and a possible approach to their study. This paper continues from the first one by investigating in detail many of the cases where curvature collineations can occur in space-time. It is based on a classification of the curvature tensor which is discussed in the first paper and reviewed briefly here. This, together with the geometrical approach favored in this paper, leads to a rather general discussion of the problem which, it is hoped, does not obscure those physical aspects of the situation that are important in Einstein's theory.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 181-187 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper attempts to give a comprehensive discussion of space-times that admit vector fields or second-order symmetric or skew-symmetric tensor fields which are covariantly constant or recurrent. The relationship between such space-times M and their holonomy group is given.
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, U.K. and Cambridge, USA : Blackwell Science Ltd
    Plant pathology 45 (1996), S. 0 
    ISSN: 1365-3059
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Inadequate species definitions present a serious problem to the pathologist working in plant hygiene or quarantine which demands urgent attention. Species concepts in the downy mildews have not kept pace with developments in evolutionary and molecular biology, or with advances in ecological genetics, because the downy mildews are obligate biotrophs that are not easily cultured in the laboratory. Existing approaches to species concepts in this group (morphometric, Ga¨umann’s ‘biological species’ and Skalicý’s ‘eco–physio–phentic’ concepts) are examined and found to be inadequate and potentially misleading. The systematic treatment of the downy mildews is beginning to benefit from the application of modern methods of systematic analysis. The contribution and potential of ultrastructure, karyotyping, sterol and fatty acid composition, isoenzyme patterns, molecular biology, numerical methods, immunoassay and hypotheses of coevolution to the development of species concepts are reviewed and their wider application is seen as a priority. The application to the downy mildews of two widespread species concepts, the biological and phylogenetic concepts, is examined in the light of the information gained from modern methods of analysis, but neither is found adequate to describe species of downy mildews as they occur in nature. Modern methods can suggest phylogenetic relationships on the basis of statistical probabilities and may also detect microevolutionary change, but it is concluded that much more information is required about individual breeding systems, gene flow, ecology, phylogeny and distribution before informed decisions about the delimitation of most species can be made. Until patterns of genetic diversity can be established, a modified phylogenetic species concept may offer one interim solution to the problem of species definition in the downy mildews.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 28 (1987), S. 1837-1839 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that for a general space-time in Einstein's theory (with the term "general'' being precisely defined) the Weyl tensor and energy-momentum tensor determine the metric up to a constant conformal factor. One of the conclusions may be interpreted as a generalization of the well-known Brinkmann theorem characterizing pp waves in vacuo.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 42 (2001), S. 347-354 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A discussion of projective symmetry in general relativity is given. Techniques are developed and used to show that null Einstein–Maxwell fields in general relativity cannot admit any proper projective symmetry. © 2001 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1466-1478 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Three-dimensional manifolds admitting Lorentz metrics are studied. The first part of the paper gives a classification of the Ricci and curvature tensors and also of the conformal (Schouten–Cotton–York) tensor. The second part of the paper investigates Killing and conformal symmetry and also the nature of the zeros of the associated vector fields. The maximum dimension of the Killing and conformal algebras is calculated. A theorem regarding the reduction of the conformal algebra to a Killing algebra of a conformally related metric is given. © 1999 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 5938-5948 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A discussion is given regarding those Lie subgroups of GL(n, R) which contain SO(n) or SO(n−1,1) as Lie subgroups. The result is applied to the theory of holonomy groups and in particular to metric and Weyl connections. Some general remarks regarding the relationship between metric connections and curvature tensors are given. © 1995 American Institute of Physics.
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