Abstract
The geometry of regular Lagrangians provides useful differential geometric models for a variety of fields, including variational calculus, electromagnetic theory, general relativity and relativistic optics, [MA]. Although the general theory of Lagrange differential geometry has been fully developed, only the so-called almost Finsler Lagrangians have been studied for purposes of applications until now. In the present paper, another class of Lagrangians, which arise in biology, are studied from a purely geometrical point-of-view, [MA].
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References
P.L. Antonelli, R.S. Ingarden and M. Matsumoto, The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology, Kluwer Academic Publishers, Dordrecht, 1993, pp. 350.
P.L. Antonelli and H. Shimada, On 1-form connections with constant coefficients, Tensor, N.S., 50 (1991), 263–275.
S. Höjö, Structures of fundamental functions of S3-like spaces, J. Math. Kyoto. Univ., 21 (1981), 787–807.
S. Höjö, On the determination of generalized Cartan connection and fundamental functions of Finsler spaces, Tensor, N.S., 35 (1981), 333–344.
S. Höjö, On some generalized connection and their applications, Proc. Romanian-Japanese Coll. on Finsler Geometry, Iasi 1984, 23–26.
S. Höjö, On generalizations of Akbar-Zadeh’s Theorem in Finsler geometry, Tensor, N.S., 37 (1982), 285–290.
R. Miron and M. Anastasiei, The Geometry of Lagrange Spaces: Theory and Applications, Kluwer Academic Publishers, Dordrecht, 1994, pp. 285.
H. Rund, The Differential Geometry of Finsler Spaces, Springer-Verlag, 1959, pp. 285.
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© 1996 Springer Science+Business Media Dordrecht
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Anastasiei, M., Antonelli, P.L. (1996). The Differential Geometry of Lagrangians which Generate Sprays . In: Antonelli, P.L., Miron, R. (eds) Lagrange and Finsler Geometry. Fundamental Theories of Physics, vol 76. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8650-4_2
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DOI: https://doi.org/10.1007/978-94-015-8650-4_2
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