Non-Euclidean Geometries

I. History

1. The Revolution of János Bolyai
András Prékopa

2. Gauss and Non-Euclidean Geometry
Jeremy Gray

3. János Bolyai’s New Face
Elemér Kiss

II. Axiomatical and Logical Aspects

4. Hyperbolic Geometry, Dimension-Free
Walter Benz

5. An Absolute Property of Four Mutually Tangent Circles
H.S.M. Coxeter

6. Remembering Donald Coxeter
Asia Ivic Weiss, William Weiss

7. Axiomatizations of Hyperbolic and Absolute Geometries
Victor Pambuccian

8. Logical Axiomatizations of Space-Time. Samples from the Literature
Hajnal Andréka, Judit X. Madarász, István Németi

III. Polyhedra, Volumes, Discrete Arrangements, Fractals

9. Structures in Hyperbolic Space
Robert Connelly

10. The Symmetry of Optimally Dense Packings
Charles Radin

11. Flexible Octahedra in the Hyperbolic Space
Hellmuth Stachel

12. Fractal Geometry on Hyperbolic Manifolds
Bernd O. Stratmann

13. A Volume Formula for Generalised Hyperbolic Tetrahedra
Akira Ushijima

IV. Tilings, Orbifolds and Manifolds, Visualization

14. The Geometry of Hyperbolic Manifolds of Dimension at Least 4
John G. Ratcliffe

15. Real-Time Animation in Hyperbolic, Spherical, and Product Geometries
Jeffrey R. Weeks

16. On Spontaneous Surgery on Knots and Links
A.D. Mednykh, V.S. Petrov

17. Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces
E. Molnár, I. Prok, J. Szirmai

V. Differential Geometry

18. Non-Euclidean Analysis
Sigurdur Helgason

19. Holonomy, Geometry and Topology of Manifolds with Grassmann Structure
Neda Bokan, Paola Matzeu, Zoran Raki?

20. Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry
Old?ich Kowalski, Masami Sekizawa

21. How Far Does Hyperbolic Geometry Generalize?
János Szenthe

22. Geometry of the Point Finsler Spaces
Lajos Tamássy

VI. Physics

23. Black Hole Perturbations
Zoltán Perjés

24. Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned
Abraham A. Ungar

Keywords: Mathematics, Geometry, History of Mathematics, Differential Geometry, Manifolds and Cell Complexes (incl. Diff.Topology), Relativity and Cosmology