32 citations · 162 across the 72 of their papers we have counts for
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On Hilbert's fourth problem
Athanase Papadopoulos
Hilbert's fourth problem asks for the construction and the study of metrics on subsets of projective space for which the projective line segments are geodesics. Several solutions o…
On Lobachevsky's trigonometric formulae
Athanase Papadopoulos
We elaborate on some important ideas contained in Lobachevsky's Pangeometry and in some of his other memoirs. The ideas include the following: (1) The trigonometric formulae, which…
Weak Minkowski Spaces
Athanase Papadopoulos, Marc Troyanov
We define the notion of weak Minkowski metric and prove some basic properties of such metrics. We also highlight some of the important analogies between Minkowski geometry and the…
Hyperbolic metrics, measured foliations and pants decompositions for non-orientable surfaces
Athanase Papadopoulos, Robert C. Penner
We provide analogues for non-orientable surfaces with or without boundary or punctures of several basic theorems in the setting of the Thurston theory of surfaces which were develo…
Torus bundles and 2-forms on the universal family of Riemann surfaces
Robin de Jong
We revisit three results due to Morita expressing certain natural integral cohomology classes on the universal family of Riemann surfaces C_g, coming from the parallel symplectic f…