Bochner-kähler metrics

Journal of the American Mathematical Society

Volumn 14, Issue 3, 2001, Pages 623-715

  Bryant, Robert L ^a  

^a DUKE UNIVERSITY   (United States)

Author keywords

Bochner tensor; K hler metrics; Momentum map; Polytope

Indexed keywords

EID: 0035609685     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0894-0347-01-00366-6     Document Type: Article

References (30)

1. M. Abreu, Kähler geometry of toric varieties and extremal metrics, Internat. J. Math. 9 (1998), 641-651. MR 99j:58047
2. V. Apostolov and P. Gauduchon, Self-dual Einstern Hermitian four-manifolds, preprint, 2000, arXiv:math.DG/0003162.
3. A. Besse, Einstein Manifolds, Springer-Verlag, New York, 1987. MR 88f:53087
4. S. Bochner, Curvature and Betti numbers, II, Ann. Math. 50 (1949), 77-93. MR 10=571f
5. S. Bochner and K. Yano, Curvature and Betti Numbers, Annals of Math. Studies, No. 32, Princeton University Press, Princeton, 1953. MR 15:989f
6. E. Cartan, Sur la structure des groupes inifinis de transformations, Ann. Éc. Norm. 3 (1904), 153-206 (Reprinted in Cartan's Collected Works, Part II.)
7. B. Y. Chen, Some topological obstructions to Bochner-Kähler metrics and their applications, J. Diff. Geom. 13 (1978), 547-558. MR 81f:32037
8. J. Deprez, et al., Classifications of Kähler manifolds satisfying some curvature conditions, Sci. Rep. Niigata Univ. Ser. A 24 (1988), 1-12. MR 89d:53045
9. A. Derdziński, Self-dual Kähler manifolds and Einstein manifolds of dimension four, Compositio Math. 49 (1983), 405-433. MR 84h:53060
10. N. Ejiri, Bochner-Kähler metrics, Bull. Sci. Math. 108 (1984), 423-436. MR 86g:53026
11. W. Fulton and J. Harris, Representation Theory, Graduate Texts in Mathematics, no. 129, Springer-Verlag New York, 1991. MR 93a:20069
12. V. Guillemin, Kaehler metrics on toric varieties, J. Diff. Geom. 40 (1994), 285-309. MR 95h:32029
13. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, Princeton, 1978. MR 80k:53081
14. Y. Kamishima, Uniformization of Kähler manifolds with vanishing Bochner tensor, Acta Math. 172 (1994), 299-308. MR 95c:53080
15. U.-H. Ki and B. H. Kim, Manifolds with Kaehler-Bochner metric, Kyungpook Math. J. 32 (1992), 285-290. MR 93m:53075
16. J. Leysen, et al., Some curvature conditions in Bochner-Kaehler manifolds, Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 65 (1987), 85-94. MR 90b:53027
17. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, vol. II, John Wiley & Sons, New York, 1963. MR 38:6501
18. K. Mackenzie, Lie algebroids and Lie pseudoalgebras, Bull. London Math. Soc. 27 (1995), 97-147. MR 96i:58183
19. M. Matsumoto, On Kählerian spaces with parallel or vanishing Bochner curvature tensor, Tensor (N.S.) 20 (1969), 25-28. MR 39:3433
20. M. Matsumoto and S. Tanno, Kählerian spaces with parallel or vanishing Bochner curvature tensor, Tensor (N.S.) 27 (1973), 291-294. MR 49:7943
21. J. Pradines, Théorie de Lie pour les groupoïdes différentiables. Calcul différenetiel dans la catégorie des groupoïdes infinitésimaux, C. R. Acad. Sci. Paris Sér. A-B 264 (1967), A245-A248. MR 35:7242
22. J. Pradines, Troisième théorème de Lie sur les groupoïdes différentiables, C. R. Acad. Sci. Paris Sér. A-B 267 (1968), A21-A23. MR 37:6969
23. C. Procesi, The invariant theory of n × n matrices, Advances in Math. 19 (1976), 306-381. MR 54:7512
24. N. Pušić, On an invariant tensor of a conformal transformation of a hyperbolic Kaehlerian space, Zb. Rad. 4 (1990), 55-64. MR 92j:53014
25. N. Pušić, On HB-flat hyperbolic Kaehlerian spaces, Mat. Vesnik 49 (1997), 35-44. MR 98i:53044
26. K. Shiga, Cohomology of Lie algebras over a manifold. I & II, J. Math. Soc. Japan 26 (1974), 324-361, 587-607. MR 51:4267, MR 51:4268
27. A. Cannas da Silva and A. Weinstein, Geometric Models for Noncommutative Algebras, University of California at Berkeley Lecture Notes, American Mathematical Society, 1999. CMP 2000:15
28. S. Tachibana and R. Liu, Notes on Kaehlerian metrics with vanishing Bochner curvature tensor, Kodai Math. Sem. Rep. 22 (1970), 313-321. MR 42:1030
29. 1 = 0, Hokkaido Math. J. 3 (1974), 129-132. MR 49:3736
30. D. Van Lindt and L. Verstraelen, A survey on axioms of submanifolds in Riemannian and Kählerian geometry, Colloq. Math. 54 (1987), 193-213. MR 89h:53115