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Gaussian surface theory, treated in Chapter V, is relative insofar as the surface metric, which changes from point to point, is induced by the metric of the surrounding higher dimensional euclidean space. For Gauss, however, the crucial point was to construct a theory of surfaces “from the inside out”, so to speak, using only concepts that relate to the surface itself, ignoring its embedding in a higher dimensional space.
KeywordsRiemannian Geometry Translation Operator Covariant Vector Parallel Translation Chapter Versus
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