The Gauss-Bonnet Formula for Hyperbolic Manifolds of Finite Volume

Geometriae Dedicata

Volumn 84, Issue 1-3, 2001, Pages 49-62

  Kellerhals, Ruth ^a   Zehrt, Thomas ^a  

^a UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

Angle sum; Euler characteristic; Generalized simplicial complex; Hyperbolic manifold; Triangulation

Indexed keywords

EID: 0042285763     PISSN: 00465755     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1010352829732     Document Type: Article

References (21)

1. Adams, C. C.: The noncompact hyperbolic 3-manifold of minimal volume, Proc. Amer. Math. Soc. 100 (1987), 601-606.
2. Allendoerfer, C. B. and Weil, A.: The Gauss-Bonnet theorem for Riemannian polyhedra, Trans. Amer. Math. Soc. 53 (1943), 101-129.
3. Besson, G., Courtois, G. and Gallot, S.: Volume et entropie minimale des espaces localement symétriques, Invent. Math. 103 (1991), 417-445.
4. Chern, S. S.: A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds, Ann Math. 45 (1944), 747-752.
5. Davis, M. W.: A hyperbolic 4-manifold, Proc. Amer. Math. Soc. 93 (1985), 325-328.
6. Epstein, D. B. A. and Penner, R. C.: Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988), 67-80.
7. Geometry II, In: E. B. Vinberg (ed.), Encyclopaedia of Math. Sci. 29, Springer-Verlag, New York, 1993.
8. Greenberg, M. J.: Lectures on Algebraic Topology, Benjamin, 1967.
9. Gromov, M.: Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982), 5-99.
10. Harder, G.: A Gauss-Bonnet formula for discrete arithmetically defined groups, Ann. Sci. École Norm. Sup. 4 (1971), 409-455.
11. Hirzebruch, F.: Topological Methods in Algebraic Geometry, Classics Math., Springer-Verlag, Berlin, 1995.
12. Hopf, H.: Die Curvatura Integra Clifford-Kleinscher Raumformen, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. (1925), 131-141.
13. Kellerhals, R.: On Schläfli's reduction formula, Math. Z. 206 (1991), 193-210.
14. Munkres, J. R.: Elementary Differential Topology, Ann. Math. Stud. 54, Princeton Univ. Press, 1966.
15. Nevanlinna, R.: Uniformisierung, Springer-Verlag, Berlin, 1967.
16. Peschl, E.: Winkelrelationen am Simplex und die Eulersche Charakteristik, München Ak. Sb. 25 (1955), 319-345.
17. Poincaré, H.: Sur la généralisation d'un théorème élémentaire de géométrie, C.R. Acad. Sci. 140 (1905), 113-117.
18. Ratcliffe, J. G.: Foundations of Hyperbolic Manifolds, Springer-Verlag, New York, 1994.
19. Ratcliffe, J. G. and Tschantz, S. T.: Volumes of hyperbolic manifolds, Preprint, 1994.
20. Rosenberg, S.: Gauss-Bonnet theorems for noncompact surfaces, Proc. Amer. Math. Soc. 86 (1982), 184-185.
21. Spivak, M.: A Comprehensive Introduction to Differential Geometry, Publish or Perish, New York, 1975.