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.
Finsler ( α ; β ) metric nonholonomic frame projectively flat
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 29 Ekim 2021 |
Kabul Tarihi | 8 Eylül 2021 |
Yayımlandığı Sayı | Yıl 2021 |