Abstract
Let U be an open region of the real number space IRn = {x = (x 1,... , x n)} of n dimensions. We shall consider a real-valued function
of 2n arguments (x i) and (y i), i = 1,..., n, which is assumed to be of class C 2 for x in U and for y unrestricted. Next, let C be a curve [a, b] → U in U of the form
where x i(t) are assumed to be of class C 1 in [a, b]. Such a curve having the fixed endpoints x(a), x(b) is called admissible.
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© 1993 Springer Science+Business Media Dordrecht
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Antonelli, P.L., Ingarden, R.S., Matsumoto, M. (1993). Finsler Metrics. In: The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology. Fundamental Theories of Physics, vol 58. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8194-3_2
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DOI: https://doi.org/10.1007/978-94-015-8194-3_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4341-2
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