On the compatibility of supermetrics with nonlinear connections

Document Type : Original Article

Author

Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht‎, ‎Iran.

Abstract

One of the Helmholtz conditions for the inverse problem of a ‎Lagrangian Mechanics is the metric compatibility of a semispray‎ ‎and the associated nonlinear connection with a generalized‎ ‎Lagrange metric‎. ‎In this paper‎, ‎with respect to the supermetric‎ ‎induced by the Hessian of the Lagrangian‎, ‎we find a family of‎ ‎nonlinear connections compatible with supermetric‎. ‎In a particular case‎, ‎when a Lagrangian superfunction‎ ‎is regular‎, ‎we have a solution for the Euler-Lagrange‎
‎superequation which‎ ‎defines a metric nonlinear connection‎.

Keywords

References

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Journal of Finsler Geometry and its Applications
Volume 4, Issue 2
December 2023
Pages 22-37

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