Part of the Universitext book series (UTX)
A Riemannian metric on a manifold M is a family of scalar products defined on each tangent space TmM and depending smoothly on m:
2.1 Definition : A Riemannian metric on M is a smooth and positive definite section g of the bundle S2T*M of the symmetric bilinear 2-forms on M.
KeywordsVector Field Riemannian Manifold Homogeneous Space Parallel Transport Klein Bottle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer-Verlag Berlin Heidelberg 1987