论文标题
导航问题和圆锥kropina歧管上的曲率特性
The navigation problems and the curvature properties on conic Kropina manifolds
论文作者
论文摘要
在本文中，我们研究了Conic Kropina歧管上的导航问题。令$ f（x，y）$为$ n $ dimensional歧管$ m $和$ v $的CONIC KROPINA度量标准，是$ f（m，f）$上的共形矢量字段，带有$ f（x，-v_ {x}）\ leq 1 $。令$ \ wideTilde {f} = \ widetilde {f}（x，y）$是带有导航数据$（f，v）$的导航问题的解决方案。我们证明，$ \ widetilde {f} $必须是randers公制，也必须是kropina公制。然后，我们建立了$ f $的某些曲率属性与新公制$ \ widetilde {f} $的相应属性之间的关系，该属性涉及s-curvature，flag曲率和ricci曲率。
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 $F(x, - V_{x})\leq 1$. Let $\widetilde{F}= \widetilde{F} (x,y)$ be the solution of the navigation problem with navigation data $(F, V)$. We prove that $\widetilde{F}$ 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 $\widetilde{F}$, which involve S-curvature, flag curvature and Ricci curvature.
