Titlebook: Differentiable Manifolds; A Theoretical Physic Gerardo F. Torres del Castillo Textbook 20121st edition Springer Science+Business Media, LLC

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Chapter 3: Bearing the Blood of FranceIn many cases, the manifolds of interest possess a metric tensor which defines an inner product between tangent vectors at each point of the manifold. Some examples are the submanifolds of an Euclidean space and the space–time, in the context of special or general relativity.

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Riemannian Manifolds,In many cases, the manifolds of interest possess a metric tensor which defines an inner product between tangent vectors at each point of the manifold. Some examples are the submanifolds of an Euclidean space and the space–time, in the context of special or general relativity.

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Lie Groups,A Lie group is a group that possesses, in addition to the algebraic structure of a group, a differentiable manifold structure compatible with its algebraic structure in the sense that the group operations are differentiable functions.

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