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Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2009, том 5
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Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds
Інший ID:
2000 Mathematics Subject Classification: 53C29; 53C22; 53C50
Посилання:
Holonomy and Projective Equivalence in 4-Dimensional Lorentz Manifolds / G.S. Hall, D.P. Lonie // Symmetry, Integrability and Geometry: Methods and Applications. — 2009. — Т. 5. — Бібліогр.: 26 назв. — англ.
Підтримка:
This paper is a contribution to the Special Issue “Elie Cartan and Differential Geometry”.
Дата:
2009
Переглядів:
394
Завантажень:
207
Анотація:
A study is made of 4-dimensional Lorentz manifolds which are projectively related, that is, whose Levi-Civita connections give rise to the same (unparameterised) geodesics. A brief review of some relevant recent work is provided and a list of new results connecting projective relatedness and the holonomy type of the Lorentz manifold in question is given. This necessitates a review of the possible holonomy groups for such manifolds which, in turn, requires a certain convenient classification of the associated curvature tensors. These reviews are provided.
