English

On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space

Differential Geometry 2022-03-02 v1

Abstract

In this paper we consider three dimensional upper half space H3\mathbb{H}^3 equipped with various Kropina metrics obtained by deformation of hyperbolic metric of H3\mathbb{H}^3 through 11-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 x3x^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.

Keywords

Cite

@article{arxiv.2203.00220,
  title  = {On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space},
  author = {Ashok Kumar and Ranadip Gangopadhyay and Bankteshwar Tiwari and Hemangi Madhusudan Shah},
  journal= {arXiv preprint arXiv:2203.00220},
  year   = {2022}
}