Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

The Calabi construction for compact Ricci flat Riemannian manifolds


Authors: Arthur E. Fischer and Joseph A. Wolf
Journal: Bull. Amer. Math. Soc. 80 (1974), 92-97
MSC (1970): Primary 53C25
DOI: https://doi.org/10.1090/S0002-9904-1974-13368-9
MathSciNet review: 0383299
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. L. Auslander, Bieberbach's theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math. (2) 71 (1960), 579-590. MR 22 #12161. MR 121423
  • 2. M. Berger, Sur les variétés d'Einstein compactes, Comptes Rendus de la IIIe Reunion du Groupement des Mathematiciens d'Expression Latine, (Namur 1965), Librairie Universitaire, Louvain, 1966, pp. 35-55. MR 38 #6502. MR 238226
  • 3. M. Berger and D. Ebin, Some decompositions of the space of symmetric tensors on a Riemannian manifold, J. Differential Geometry 3 (1969), 379-392. MR 42 #993. MR 266084
  • 4. Ludwig Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume, Math. Ann. 70 (1911), no. 3, 297–336 (German). MR 1511623, https://doi.org/10.1007/BF01564500
  • 5. S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776-797. MR 8, 230. MR 18022
  • 6. E. Calabi, Closed, locally euclidean, 4-dimensional manifolds, Bull. Amer. Math. Soc. 63 (1957), Abstract 295, 135.
  • 7. J. Cheeger and D. Gromoll, The splitting theorem for manifolds of non-negative Ricci curvature, J. Differential Geometry 6 (1971), 119-128. MR 303460
  • 8. A. Fischer and J. Marsden, Submanifolds of riemannian metrics with prescribed scalar curvature, Bull. Amer. Math. Soc. (to appear). MR 346839
  • 9. A. Fischer and J. A. Wolf, The structure of compact Ricci flat riemannian manifolds, (to appear). MR 377759
  • 10. E. Nelson, Tensor analysis, Princeton Univ. Press, Princeton, N.J., 1967.
  • 11. J. A. Schouten and D. J. Struik, On Some Properties of General Manifolds Relating to Einstein’s Theory of Gravitation, Amer. J. Math. 43 (1921), no. 4, 213–216. MR 1506446, https://doi.org/10.2307/2370191
  • 12. T. J. Willmore, On compact Riemannian manifolds with zero Ricci curvature, Proc. Edinburgh Math. Soc. (2) 10 (1956), 131-133. MR 17, 783. MR 75646
  • 13. J. A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry 2 (1968), 421-446. MR 40 #1939. MR 248688
  • 14. J. A. Wolf, Spaces of constant curvature, 2nd ed., J. A. Wolf, Berkeley, 1972.
  • 15. K. Yano and S. Bochner, Curvature and Betti numbers, Ann. of Math. Studies, no. 32, Princeton Univ. Press, Princeton, N.J., 1953. MR 15, 989. MR 62505
  • 16. S. Yau, Compact flat Riemannian manifolds, J. Differential Geometry 6 (1972), 395-402. MR 305309

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 53C25

Retrieve articles in all journals with MSC (1970): 53C25


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1974-13368-9

American Mathematical Society