Isometries of two dimensional Hilbert Geometries

2014/09/19 by Matveev, Vladimir S., Troyanov, Marc
#51F #53C60 #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1409.5611

Abstract

We prove that any isometry between two dimensional Hilbert geometries is a projective transformation unless the domains are interiors of triangles.

Related

• Isometries of the Hilbert Metric
• Isometries of polyhedral Hilbert geometries
• Isometries of infinite dimensional Hilbert geometries
• Extension of isometries in real Hilbert spaces
• Partial Isometries Between Hilbert Modules and Their Compositions