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A Poincaré Potential and Holomorphic Killing Vector Fields

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In this paper, we will show that if there is a locally defined potential function of the Poincar\'e metric with constant gradient length, then the length is determined by the Gaussian curvature. In order to show, we will study a holomorphic Killing vector field generated by the potential and its geometry. \end{abstract}

Abstract

In this paper, we will show that if there is a locally defined potential function of the Poincar\'e metric with constant gradient length, then the length is determined by the Gaussian curvature. In order to show, we will study a holomorphic Killing vector field generated by the potential and its geometry. \end{abstract}

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