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Published in:
2020 | OriginalPaper | Chapter
6. Riemannian Manifolds
Author : Gerardo F. Torres del Castillo
Published in: Differentiable Manifolds
Publisher: Springer International Publishing
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Abstract
A differentiable manifold is properly Riemannian if it is endowed with a tensor field (known as metric tensor) which defines an inner product between tangent 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.