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 equipped with various Kropina metrics obtained by deformation of hyperbolic metric of through -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 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}
}