Riemannian Manifolds

Gerardo F. Torres del Castillo ()
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Gerardo F. Torres del Castillo: Benemérita Universidad Autónoma de Puebla, Instituto de Ciencias

Chapter Chapter 6 in Differentiable Manifolds, 2020, pp 141-202 from Springer

Abstract: 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.

Date: 2020
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DOI: 10.1007/978-3-030-45193-6_6

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