Abstract
Geodesics are curves in n-surfaces which play the same role as do straight lines in ℝn. Before formulating a precise definition, we must introduce the proccss of differentiation of vector fields and functions defined along parametrized curves. In order to allow the possibility that such vector fields and functions may take on different values at a point where a parametrized curve crosses itself, it is convenient to regard these fields and functions to be defined on the parameter interval rather than on the image of the curve.
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). Geodesics. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_7
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_7
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