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On the compatibility of supermetrics with nonlinear connections | ||
| Journal of Finsler Geometry and its Applications | ||
| دوره 4، شماره 2، اسفند 2023، صفحه 22-37 اصل مقاله (280.12 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.22098/jfga.2023.13513.1094 | ||
| نویسنده | ||
| Esmaeil Azizpour* | ||
| Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht‎, ‎Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Horizontal endomorphism؛ Finsler supermanifolds؛ Canonical nonlinear connection؛ Supermetric | ||
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آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 52 |
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