DOI: 10.68381/jca18007 ISSN: 0944-6532
A Weighted Steiner Minimal Tree for Convex Quadrilaterals on the Two-Dimensional K-Plane
Anastasios Zachos
We provide a method to find a weighted Steiner minimal tree for convex quadrilaterals on a two-dimensional hemisphere of radius
\frac{1}{\sqrt{K}}
1
K
, for
K>0
K
>
0
and the two dimensional hyperbolic plane of constant Gaussian Curvature K, for
K<0
K
<
0
by introducing a method of cyclical differentiation of the objective function with respect to four variable angles. By applying this method, we find a generalized solution to a problem posed by C.F. Gauss in the spirit of weighted Steiner trees.