New York Journal of Mathematics
Volume 25 (2019), 107-122


Jenö Szirmai

Bisector surfaces and circumscribed spheres of tetrahedra derived by translation curves in Sol geometry

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Published: January 5, 2019.
Keywords: Thurston geometries, Sol geometry, translation-like bisector surface.
Subject: 53A20, 53A35, 52C35, 53B20.

In the present paper we study the Sol geometry, which is one of the eight homogeneous Thurston 3-geometries. We determine the equation of the translation-like bisector surface of any two points. We prove that the isosceles property of a translation triangle is not equivalent to two angles of the triangle being equal, and that the triangle inequalities do not remain valid for translation triangles in general.



Author information

Jenö Szirmai:
Budapest University of Technology and Economics
Institute of Mathematics, Department of Geometry
Budapest, P. O. Box: 91, H-1521, Hungary