On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space

Abstract

In this paper we consider three dimensional upper half space H 3 equipped with various Kropina metrics obtained by deformation of hyperbolic metric of 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.