SUT Journal of Mathematics Vol. 41, No. 1 (2005), 95
Corrigendum to
‘On the Killing vector fields of generalized metrics’
(in SUT Journal of Mathematics,
Vol. 40, No. 2 (2004), 133 – 156)
Rezs˝o L. Lovas
(Received April 22, 2005)
In §9, the Killing vector fields of Poincar´e’s hyperbolic upper half-plane model should have the form
X =[α((u1)2− (u2)2)+ βu1+ γ] ∂
∂u1 +
(
2αu1+ β)u2 ∂ ∂u2
with some α, β, γ ∈ R. The upper half-plane may be identified with the set of complex numbers with positive imaginary part. Suppose that α 6= 0, and introduce the notation k :=√|β2/4− αγ|. Then the integral curves of X are
given by z(t) =−k α c cosh kt− sinh kt c sinh kt− cosh kt− β 2α if β2 4 − αγ > 0, z(t) =−k α c cos kt + sin kt c sin kt− cos kt− β 2α if β2 4 − αγ < 0, z(t) =− 1 αt + c− β 2α if β2 4 − αγ = 0 with c∈ C such that Im c > 0.
Rezs˝o L. Lovas
Institute of Mathematics, University of Debrecen H – 4010 Debrecen, P. O. Box 12, Hungary
