• East Asian mathematical journal
• /
• 제39권1호
• /
• pp.11-21
• /
• 2023

Non-trivial automorphisms of the unit disc in the complex plane can be classified by three classes; elliptic, parabolic and hyperbolic automorphisms. This classification is due to a representation in the projective special linear group of the real field, or in terms of fixed points on the closure of the unit disc. In this paper, we will characterize this classification by the distance function of the Poincaré metric on the interior of the unit disc.

• 대한수학회지
• /
• 제57권6호
• /
• pp.1335-1345
• /
• 2020

We will show a rigidity of a Kähler potential of the Poincaré metric with a constant length differential.

• 충청수학회지
• /
• 제22권4호
• /
• pp.771-776
• /
• 2009

Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).