Abstract
In this section, we use the method of differential forms to describe the first variation. There is another approach which uses vector fields and covariant differentiation. That is explored in a series of guided exercises at the end of 5.2. (Those exercises involve the second variation as well.) A systematic self-contained account can also be found in [BC1].
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References
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Bao, D., Chern, SS., Shen, Z. (2000). Variations of Arc Length, Jacobi Fields, the Effect of Curvature. In: An Introduction to Riemann-Finsler Geometry. Graduate Texts in Mathematics, vol 200. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1268-3_5
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DOI: https://doi.org/10.1007/978-1-4612-1268-3_5
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