Abstract
We have discussed Gauss’ Theorema Egregium and the Gauss and Codacci equations in Chapter 2 in their original formulation of a two-dimensional surface imbedded in the three-dimensional Euclidean space. The metric and the covariant derivative on the surface was induced from the derivative of the ambient Euclidean space. The great discovery was that the metric and covariant derivative referred only to the surface, that is, intrinsic quantities. This result led to the Riemannian geometry we know.
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(2009). Special Topics. In: Spacetime, Geometry and Gravitation. Progress in Mathematical Physics, vol 56. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9971-9_16
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DOI: https://doi.org/10.1007/978-3-7643-9971-9_16
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-9970-2
Online ISBN: 978-3-7643-9971-9
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