Abstract
In Chapter 7 we defined geodesics as “straightest curves” in an n-surface. In this chapter we shall examine the role of geodesics as “shortest curves” We begin by using a technique of the calculus of variations analogous to the one we used in Chapter 18 to study minimal surfaces. Now, however, we shall vary parametrized curves rather than parametrized surfaces
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© 1979 Springer-Verlag New York Inc.
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Thorpe, J.A. (1979). The Exponential Map. In: Elementary Topics in Differential Geometry. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6153-7_19
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DOI: https://doi.org/10.1007/978-1-4612-6153-7_19
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6155-1
Online ISBN: 978-1-4612-6153-7
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