Geodesic
Autoparallel Deviation in the Geometry of Lyra
Canadian mathematical bulletin, Tome 3 (1960) no. 3, pp. 263-271

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

One of the fruitful tools for examining the properties of a Riemannian manifold is the study of “geodesic deviation”. The manner in which a vector, representing the displacement between points on two neighbouring geodesies, behaves gives an indication of the difference between the manifold and an Euclidean space. The study is essentially a geometrical approach to the second variation of the lengthintegral in the calculus of variations [1]. Similar considerations apply in the geometry of Lyra [2] but as we shall see, appropriate analytical modifications must be made. The approach given here is modelled after that of Rund [3] which was originally designed to deal with a Finsler manifold but which applies equally well to the present case. 
Vanstone, J. R. Autoparallel Deviation in the Geometry of Lyra. Canadian mathematical bulletin, Tome 3 (1960) no. 3, pp. 263-271. doi: 10.4153/CMB-1960-033-8
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[1] 1. Blaschke, W., Differential Geometry, (New York, 1945) p. 212, et seq. Google Scholar

[2] 2. Lyra, G., Über eine Modifikation der riemannschen Geometrie, Math, Z. 54 (1951), 52-64. Google Scholar

[3] 3. Rund, H., The Differential Geometry of Finsler Spaces, Springer-Verlag (Berlin-Gottingen-Heidelberg, 1959), 111-119. Google Scholar

[4] 4. Scheibe, E., Über einen verallgemeinerten affinen Zusammenhang, Math, Z, 57 (1952), 65-74. Google Scholar

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