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

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Lie Groups,f differentiable manifold. Two examples are the isometries of a Riemannian manifold and the symmetries of a second-order ODE, considered in Sects. . and ., respectively. In this chapter we shall study these groups by themselves, combining their algebraic and differentiable structures. One of the mai

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Graduate Texts in Contemporary Physicsnd ., respectively. In this chapter we shall study these groups by themselves, combining their algebraic and differentiable structures. One of the main results of this combination is the fact that each of these groups has an associated Lie algebra which almost entirely determines the group.

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Textbook 2020Latest editionrential geometry, and Hamiltonian mechanics..The first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequent

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Connections, Riemannian structure or is a Lie group. The properties imposed on a connection have their origin in the study of two-dimensional surfaces in the three-dimensional Euclidean space and lead to the concept of curvature.