HARMONIC TRANSFORMATIONS OF THE HYPERBOLIC PLANE

• 발행기관: 충청수학회
• 저자명: Joon Sik Park
• 간행물 정보: 『Journal of the Chungcheong Mathematical Society』Volume 22, No. 4, 771~776쪽, 전체 6쪽
• 주제분류: 자연과학 > 자연과학일반
• 파일형태: PDF
• 발행일자: 2009.12.30

영문 초록

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).

목차

1. Introduction

2. Harmonic transformations of the hyperbolic plane

References