Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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HARMONIC TRANSFORMATIONS OF THE HYPERBOLIC PLANE

  • Park, Joon-Sik (Department of Mathematics, Pusan University of Foreign Studies)
  • Received : 2009.09.04
  • Accepted : 2009.11.19
  • Published : 2009.12.30
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Abstract

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).

Keywords

References

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