A transformation of the Finsler metric by an h-vector (Q1118827)

Let \(F^ n=(M,L)\) and \(F^{*n}=(M,L^*)\) be two Finsler spaces such that \(L^{*2}(x,y)=L^ 2(x,y)+(X_ i(x)y^ i)^ 2.\) In this paper relations between the Finsler tensor fields \(\ell^*_ i\), \(g^*_{ij}\), \(C^*_{ijk}\) and \(\ell_ i\), \(g_{ij}\), \(C_{ijk}\) are studied as well as relations between the tensors induced by them on hypersurfaces \(\tilde F^{n-1}\) and \(\tilde F^{*n-1}\) of \(F^ n\) and \(F^{*n}\) respectively, assuming that \(X_ i\) is a tangential covector field.