Conformal correspondence of Finslerian hypersurfaces
Let \(F^ n=(M^ n,L)\) and \(\bar F{}^ n=(M^ n,\bar L)\) be two Finsler spaces with the same underlying manifold \(M^ n\) where \(L\to \bar L=e^{\sigma (x)}L\) is a conformal change of Finsler metric. Then we get two Finsler hypersurfaces \(F^{n-1}\) and \(\bar F{}^{n-1}\) on a closed submanifold \(M^{n-1}\) of \(M^ n\) which are conformal with the same conformal factor \(\sigma\) (x). The authors consider conformal correspondences of various geometrical entities of \(F^{n-1}\) and \(\bar F{}^{n-1}\) based on \textit{M. Hashiguchi}'s theory of conformal change [J. Math. Kyoto Univ. 16, 25-50 (1976; Zbl 0328.53014)] and the reviewer's systematic treatment of Finsler hypersurfaces [ibid. 25, 107- 144 (1985; Zbl 0567.53025)].
scientific article; zbMATH DE number 3990275