Isoparametric Hypersurfaces in a Class of Conic Kropina Manifolds by Navigation Data

In this paper, we study the isoparametric hypersurfaces in a class of conic Kropina manifolds. For a conic Kropina metric F(x, y) on a manifold M with navigation data (h, W), and a vector field V with $$F(x,-V)=1$$ , let $$\tilde{F}=\tilde{F}(x, y)$$ be the solution of navigation data (F, V). By studying the principal curvatures of anisotropic submanifolds in Kropina space $$(M, \tilde{F})$$ with the navigation data (h, W), we find that Kropina space $$(M, \tilde{F}, d\mu _{BH})$$ and the corresponding Riemannian space (M, h) have the same isoparametric hypersurfaces. Moreover, we give a complete classification of isoparametric hypersurfaces in Kropina space $$(M, \tilde{F}, d\mu _{BH})$$ with constant flag curvature.