Abstract
We begin our presentation of differential-geometric structures with the one whose origins are most closely tied to the way the subject was developed by Gauss and Riemann, and that carries the name of the latter. The concepts of Riemannian geometry are familiar: length, angle, distance, and curvature, among others. Historically tied to the origins of differential geometry, and with such familiar concepts, Riemannian geometry is often presented in textbooks as being synonymous with differential geometry itself, instead of as one differential-geometric structure among many.
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Notes
- 1.
Quoted in [[10], p. 15].
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McInerney, A. (2013). Riemannian Geometry. In: First Steps in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7732-7_5
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DOI: https://doi.org/10.1007/978-1-4614-7732-7_5
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