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New derivation operators in dual Finsler geometry
Corresponding Author(s) : COSMIN BUCĂTARU
Student Thinkers and Advanced Research,
Vol. 3 No. 1 (2024): Proceedings of the 7th International Conference XGEN
Abstract
In this paper work I will introduce the dynamical covariant derivative operator on the dual space of a given Finsler space using the idea of Legendre duality between the lagrangian formalism and the hamiltonian formalism. Making use of this new operator introduced I will proof that the solution curve equations and their deviations have an elegant geometrical expression.
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- I. Bucătaru, R. Miron, Finsler-Lagrange Geometry. Applications to dynamical systems., Editura Academiei Române, 2007, 1-142.
- R. Miron, D. Hrimiuc, H. Shimada, S.V. Sabău, The Geometry of Hamilton and Lagrange spaces, Kluwer Academic Publishers, New York, SUA, 2001.
- A. Bejancu, H. Farran, Geometry of Pseudo-Finsler Submanifolds, Springer, 2000.
- 1. D. Bao, S.-S. Chen, Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, New York, 2000.
- 2. V.I. Arnold, Metodele matematice ale mecanicii clasice, Editura Științifică și Pedagogică, București, 1980.
References
I. Bucătaru, R. Miron, Finsler-Lagrange Geometry. Applications to dynamical systems., Editura Academiei Române, 2007, 1-142.
R. Miron, D. Hrimiuc, H. Shimada, S.V. Sabău, The Geometry of Hamilton and Lagrange spaces, Kluwer Academic Publishers, New York, SUA, 2001.
A. Bejancu, H. Farran, Geometry of Pseudo-Finsler Submanifolds, Springer, 2000.
1. D. Bao, S.-S. Chen, Z. Shen, An Introduction to Riemann-Finsler Geometry, Springer, New York, 2000.
2. V.I. Arnold, Metodele matematice ale mecanicii clasice, Editura Științifică și Pedagogică, București, 1980.