The Randers \(\beta\)-change of More Generalized M-th Root Metrics


Authors

Abolfazl Taleshian - Department of Mathematics,Faculty of Mathematical Sciences,University of Mazandaran,Babolsar,Iran. Dordi Mohamad Saghali - Department of Mathematics,University of Mazandaran,Mazandaran,Babolsar,Iran.


Abstract

A change of Finsler metric \(F(x,y)\rightarrow \bar{F}(x,y)\) is called a Randers \(\beta\)-change of \(F\), if \(\bar{F}(x,y) = F(x,y) + \beta(x,y)\), where \(\beta(x,y)=b_i(x)y^i\) is a one-form on a smooth manifold \(M\). The purpose of the present paper is devoted to studying the conditions for more generalized m-th root metrics \(\tilde{F}_1= \sqrt{A_1^{\frac{2}{m_1}}+B_1+C_1}\) and \(\tilde{F}_1= \sqrt{A_2^{\frac{2}{m_2}}+B_2+C_2}\), when is established Randers \(\beta\)-change.


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