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

Authors : Laurianloan PISCORAN

Pages : 231-238

Doi:10.36890/iejg.973879

View : 46 | Download : 10

Publication Date : 2021-10-29

Article Type : Research Paper

Abstract :Recently, in paper [14], we have introduced the following deformed $insert ignore into journalissuearticles values(\alpha, \beta);$-metric: $$ F_{\epsilon}insert ignore into journalissuearticles values(\alpha,\beta);=\frac{\beta^{2}+\alpha^{2}insert ignore into journalissuearticles values(a+1);}{\alpha}+\epsilon\beta $$ 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 $a\in \leftinsert ignore into journalissuearticles values(\frac{1}{4},+\infty\right);$ is a real positive scalar. The aim of this paper is to find the nonholonomic frame for this important kind of $insert ignore into journalissuearticles values(\alpha, \beta);$-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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