The Generalized Randers Change of the More Generalized m-th Root Metrics

A change of Finsler metric F(x,y)→F (x,y) is called a generalized Randers change of F, if F (x,y)=F(x,y)+b_i (x,y)y^i, where b_i (x,y) is h-vector in (M,F). The purpose of the present paper is devoted to studying the conditions for more generalized m-th root metrics F _1=√(〖A_1〗^(2/m_1 )+B_1 )+ C_1 and F _2=√(〖A_2〗^(2/m_2 )+B_2 )+〖 C〗_2, when is established generalized Randers change and m_1,m_2 are even numbers. Then, we prove that under these conditions generalized Randers metric reduces to Randers metric. Finally, in the special case, we will give conditions for more generalized F _1,F _2, when is established Randers and conformal β-changes for the case of m_1,m_2 are even numbers.