Titlebook: Differentiable Manifolds; A Theoretical Physic Gerardo F. Torres del Castillo Textbook 2020Latest edition Springer Nature Switzerland AG 20

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Gerardo F. Torres del CastilloIntroduces differentiable manifolds using a theoretical physics approach.Includes applications to differential geometry and general relativity.Expands on the first edition with additional examples, mo

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Lecture Notes in Computer Science possess the structure of a normed vector space. Recall that the differentiability of a function of . to . means that around each interior point of its domain the function can be approximated by a linear transformation, but this requires the notions of linearity and distance, which are not present i

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6 Repudiative Information Retrievalntiable manifold, there is a one-to-one relation between vector fields and families of transformations of the manifold onto itself. This relation is essential in the study of various symmetries, as shown in Chaps. 4, 6 and 8, and in the relationship of a Lie group with its Lie algebra, treated in Ch

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7 Digital Rights Management for PIRield acquires its simplest expression. Just as a vector field defines a family of curves such that through each point of the manifold there passes one of these curves, it is shown that under certain conditions, a set of vector fields (or of 1-forms) defines a family of submanifolds of a fixed dimens

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6 Repudiative Information Retrievaltangent vectors at each point of the manifold. In a properly Riemannian manifold we can define lengths, areas, etc., can relate vectors with covectors, and introduce many of the geometric concepts present in the Euclidean spaces.