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Covariant Derivatives

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Comparison Finsler Geometry

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Abstract

In this chapter, we revisit the geodesic equation and give an appropriate definition of covariant derivatives of vector fields (associated with the Chern connection). Our argument will be heuristic and is motivated by a Riemannian characterization.

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References

  1. Anastasiei, M.: A historical remark on the connections of Chern and Rund. In: Bao, D., Chern, S.-S., Shen, Z. (eds.) Finsler Geometry. Contemporary Mathematics, vol. 196, pp. 171–176. American Mathematical Society, Providence, RI (1996)

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Ohta, Si. (2021). Covariant Derivatives. In: Comparison Finsler Geometry. Springer Monographs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-80650-7_4

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