论文标题
在浸入变形双曲线kropina空间中的旋转的最小表面上
On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space
论文作者
论文摘要
在本文中，我们考虑了三维上半空间$ \ mathbb {h}^3 $，配备了各种kropina度量，该指标通过$ \ mathbb {h}^3 $至$ 1 $ forms的双曲线指标的变形而获得，并获得了一个偏差方程，并获得了特征在其中的最小表面的偏差方程。我们证明，只有在沿$ x^3 $方向变形时，才能获得这种最小表面。然后，我们对这种最小表面进行了分类，并表明这些表面的标志曲率始终是非阳性的。我们还获得了该表面的测量学。特别是，因此，此类表面既没有前向共轭点，也没有前进。
In this paper we consider three dimensional upper half space $\mathbb{H}^3 $ equipped with various Kropina metrics obtained by deformation of hyperbolic metric of $\mathbb{H}^3$ through $1$-forms and obtain a partial differential equation that characterizes minimal surfaces immersed in it. We prove that such minimal surfaces can only be obtained when the hyperbolic metric is deformed along $x^3$ direction. Then we classify such minimal surfaces and show that flag curvature of these surfaces is always non-positive. We also obtain the geodesics of this surface. In particular, it follows that such surfaces neither have forward conjugate points nor they are forward complete.
