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András Prékopa and Emil Molnár
i-xiii
Front matter
3-93
I / History
3-59
The Revolution of János Bolyai
61-80
Gauss and Non-Euclidean Geometry
81-93
János Bolyai’s New Face
97-185
II / Axiomatical and Logical Aspects
97-107
Hyperbolic Geometry, Dimension-Free
109-114
An Absolute Property of Four Mutually Tangent Circles
115-118
Remembering Donald Coxeter
119-153
Axiomatizations of Hyperbolic and Absolute Geometries
155-185
Logical Axiomatizations of Space-Time. Samples from the Literature
189-265
III / Polyhedra, Volumes, Discrete Arrangements, Fractals
189-196
Structures in Hyperbolic Space
197-207
The Symmetry of Optimally Dense Packings
209-225
Flexible Octahedra in the Hyperbolic Space
227-247
Fractal Geometry on Hyperbolic Manifolds
249-265
A Volume Formula for Generalised Hyperbolic Tetrahedra
269-363
IV / Tilings, Orbifolds and Manifolds, Visualization
269-286
The Geometry of Hyperbolic Manifolds of Dimension at Least 4
287-305
Real-Time Animation in Hyperbolic, Spherical, and Product Geometries
307-319
On Spontaneous Surgery on Knots and Links
321-363
Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces
367-461
V / Differential Geometry
367-384
Non-Euclidean Analysis
385-405
Holonomy, Geometry and Topology of Manifolds with Grassmann Structure
407-426
Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry
427-444
How Far Does Hyperbolic Geometry Generalize?
445-461
Geometry of the Point Finsler Spaces
465-506
VI / Physics
465-485
Black Hole Perturbations
487-506
Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned
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