Nonholonomic Frame for a Deformed $(\alpha,\beta )$-metric

Year 2021, , 231 - 238, 29.10.2021

Laurian-loan Pıscoran

https://doi.org/10.36890/iejg.973879

Abstract

Recently, in paper [14], we have introduced the following deformed $(\alpha, \beta)$-metric:
$$
F_{\epsilon}(\alpha,\beta)=\frac{\beta^{2}+\alpha^{2}(a+1)}{\alpha}+\epsilon\beta
$$
where $\alpha=\sqrt{a_{ij}y^{i}y^{j}}$ is a Riemannian metric; $\beta=b_{i}y^{i}$ is a 1-form, $\left|\epsilon\right|<2\sqrt{a+1}$ is a real parameter and $a\in \left(\frac{1}{4},+\infty\right)$ is a real positive scalar.
The aim of this paper is to find the nonholonomic frame for this important kind of $(\alpha, \beta)$-metric and also to investigate the Frobenius norm for the Hessian generated by this kind of metric.

Keywords

Finsler ( α ; β ) metric, nonholonomic frame, projectively flat

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