The navigation problems and the curvature properties on conic Kropina manifolds

Abstract

In this paper, we study navigation problems on conic Kropina manifolds. Let $F(x,y)$ be a conic Kropina metric on an $n$-dimensional manifold $M$ and $V$ be a conformal vector field on $(M,F)$ with $F(x,-V_x)\le 1$. Let $\tilde{F}=\tilde{F}(x,y)$ be the solution of the navigation problem with navigation data $(F,V)$. We prove that $\tilde{F}$ must be either a Randers metric or a Kropina metric. Then we establish the relationships between some curvature properties of $F$ and the corresponding properties of the new metric $\tilde{F}$, which involve S-curvature, flag curvature and Ricci curvature.

References in corpus (1)

• On projective two-dimensional Finsler spaces with special metric