학술저널
HARMONIC TRANSFORMATIONS OF THE HYPERBOLIC PLANE
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 22, No. 4
-
2009.12771 - 776 (6 pages)
- 0
Let (H, g) denote the upper half plane in R2 with the Riemannian metric g := ((dx)2 + (dy)2)/y2. First of all we get a necessary and sufficient condition for a diffeomorphism of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism of (H, g) is a harmonic function, then the following facts are equivalent: (1) is a harmonic map; (2) is an affine transformation; (3) is an isometry (motion).
1. Introduction
2. Harmonic transformations of the hyperbolic plane
References
(0)
(0)