Geodesic
A Study of Tensors which Characterize a Hypersurface of a Finsler Space
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1025-1036

Voir la notice de l'article provenant de la source Cambridge University Press

The literature on Finsler geometry contains more than one definition for the normal curvature vector of a hypersurface and for coefficients of the second fundamental form; see Berwald (1), Davies (3), and Rund (5). In the first case this situation has arisen from the basically different approach to the subject adopted by the authors; Davies, following the locally Euclidean school and Rund the locally Minkowskian theory. In both cases, a comparison of the definitions shows that they are linked by expressions in a vector Mα which was introduced in the paper by Rund (7). 
Brown, Gillian M. A Study of Tensors which Characterize a Hypersurface of a Finsler Space. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 1025-1036. doi: 10.4153/CJM-1968-100-5
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[1] 1. Berwald, L., Uber die Hauptkrûmmungen einer Flàche im dreidimensionalen Finslerschen Raum, Mh. Math. Phys. 43 (1936), 1–14. Google Scholar

[2] 2. Berwald, L., Untersuchung der Kriimmung allgemeiner metrischer Ràume auf Grund des in ihnen herrschenden Parallelismus, Math. Z. 25 (1926), 40–73. Google Scholar

[3] 3. Davies, E. T., Subspaces of a Finsler space, Proc. London Math. Soc. (2) 49 (1947), 19–39. Google Scholar

[4] 4. Deicke, A., Ùber die Finsler-Ràume mit Ai - 0, Arch. Math. 4 (1953), 45–51. Google Scholar

[5] 5. Rund, H., Differential geometry of Finsler spaces (Springer-Verlag, Berlin, 1959).10.1007/978-3-642-51610-8 Google Scholar | DOI

[6] 6. Rund, H., Curvature properties of hyper surf aces of Finsler and Minkowskian spaces, Tensor N.S.) 14 (1963), 226–244. Google Scholar

[7] 7. Rund, H., Intrinsic and induced curvature theories of subspaces of a Finsler space, Tensor (N.S.) 16 (1965), 294–312. Google Scholar

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