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].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H. Akbar-Zadeh, Sur les espaces de Finsler à courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci. (5) 74 (1988), 281–322.
D. Bao and S. S. Chern, On a notable connection in Finsler geometry, Houston J. Math. 19 (1993), 135–180.
J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North Holland/American Elsevier, 1975.
P. Dazord, Propriétés globales des géodésiques des Espaces de Finsler, Theses, Université de Lyon, 1969.
M. Matsumoto, Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press, Japan, 1986.
J. H. C. Whitehead, Convex regions in the geometry of paths, Quarterly J. Math. Oxford, Ser. 3 (1932), 33–42.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1268-3_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7070-6
Online ISBN: 978-1-4612-1268-3
eBook Packages: Springer Book Archive