Abstract
In this chapter we officially define Riemannian metrics and construct some of the elementary objects associated with them. At the end of the chapter, we introduce three classes of highly symmetric “model” Riemannian manifolds—Euclidean spaces, spheres, and hyperbolic spaces—to which we will return repeatedly as our understanding deepens and our tools become more sophisticated.
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© 1997 Springer-Verlag New York, Inc.
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Lee, J.M. (1997). Definitions and Examples of Riemannian Metrics. In: Riemannian Manifolds. Graduate Texts in Mathematics, vol 176. Springer, New York, NY. https://doi.org/10.1007/0-387-22726-1_3
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DOI: https://doi.org/10.1007/0-387-22726-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98322-6
Online ISBN: 978-0-387-22726-9
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