Symmetries and Curvature Structure in General Relativity (World Scientific Lecture Notes in Physics) by G. S. Hall (PDF)

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This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein’s theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.

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Product description レビュー presents a wealth of results on the geometry of four-dimensional space-times in a well organized and carefully presented form — General Relativity and Gravitation “General Relativity and Gravitation”

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