The Calabi construction for compact Ricci flat Riemannian manifolds
HTML articles powered by AMS MathViewer
- by Arthur E. Fischer and Joseph A. Wolf PDF
- Bull. Amer. Math. Soc. 80 (1974), 92-97
References
- Louis Auslander, Bieberbach’s theorems on space groups and discrete uniform subgroups of Lie groups, Ann. of Math. (2) 71 (1960), 579–590. MR 121423, DOI 10.2307/1969945
- M. Berger, Sur les variétés d’Einstein compactes, Comptes Rendus de la IIIe Réunion du Groupement des Mathématiciens d’Expression Latine (Namur, 1965) Librairie Universitaire, Louvain, 1966, pp. 35–55 (French). MR 0238226
- 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 266084, DOI 10.4310/jdg/1214429060
- Ludwig Bieberbach, Über die Bewegungsgruppen der Euklidischen Räume, Math. Ann. 70 (1911), no. 3, 297–336 (German). MR 1511623, DOI 10.1007/BF01564500
- S. Bochner, Vector fields and Ricci curvature, Bull. Amer. Math. Soc. 52 (1946), 776–797. MR 18022, DOI 10.1090/S0002-9904-1946-08647-4 6. E. Calabi, Closed, locally euclidean, 4-dimensional manifolds, Bull. Amer. Math. Soc. 63 (1957), Abstract 295, 135.
- Jeff Cheeger and Detlef Gromoll, The splitting theorem for manifolds of nonnegative Ricci curvature, J. Differential Geometry 6 (1971/72), 119–128. MR 303460
- Arthur E. Fischer and Jerrold E. Marsden, Manifolds of Riemannian metrics with prescribed scalar curvature, Bull. Amer. Math. Soc. 80 (1974), 479–484. MR 346839, DOI 10.1090/S0002-9904-1974-13457-9
- Arthur E. Fischer and Joseph A. Wolf, The structure of compact Ricci-flat Riemannian manifolds, J. Differential Geometry 10 (1975), 277–288. MR 377759 10. E. Nelson, Tensor analysis, Princeton Univ. Press, Princeton, N.J., 1967.
- 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, DOI 10.2307/2370191
- T. J. Willmore, On compact Riemannian manifolds with zero Ricci curvature, Proc. Edinburgh Math. Soc. (2) 10 (1956), 131–133. MR 75646, DOI 10.1017/S0013091500021544
- Joseph A. Wolf, Growth of finitely generated solvable groups and curvature of Riemannian manifolds, J. Differential Geometry 2 (1968), 421–446. MR 248688 14. J. A. Wolf, Spaces of constant curvature, 2nd ed., J. A. Wolf, Berkeley, 1972.
- K. Yano and S. Bochner, Curvature and Betti numbers, Annals of Mathematics Studies, No. 32, Princeton University Press, Princeton, N. J., 1953. MR 0062505
- Shing Tung Yau, Compact flat Riemannian manifolds, J. Differential Geometry 6 (1971/72), 395–402. MR 305309
Additional Information
- 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