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arXiv · 2203.00220

On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space

Ashok Kumar·Ranadip Gangopadhyay·Bankteshwar Tiwari·Hemangi Madhusudan Shah
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Abstract

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.

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Ashok Kumar, Ranadip Gangopadhyay, Bankteshwar Tiwari, Hemangi Madhusudan Shah. 2022-03-01. On Minimal Surfaces of Revolutions Immersed in Deformed Hyperbolic Kropina Space. https://arxiv.org/abs/2203.00220

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