A bochner theorem and applications

Duke Mathematical Journal

Volumn 91, Issue 2, 1998, Pages 381-392

  Rong, Xiaochun ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0039969440     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-98-09116-5     Document Type: Article

References (36)

1. U. Abrech, Uber das glatten Riemannn scher metriken, Habilitationesschrift, Reinischen Friedrisch-Wilhelms-Universitat, Bonn, 1988.
2. a-compactness for manifolds with Ricci curvature and injectivity radius bounded below, J. Differential Geom. 35 (1992), 265-281.
3. S. Bando, Real analyticity of solutions of Hamilton’s equation, Math. Z. 195 (1987), 93-97.
4. J. Bemelmans, [MJ Min-Oo, and E. Ruh, Smoothing Riemannian metrics, Math. Z. 188 (1994), 69-74.
5. G. Bredon, Introduction to compact transformation groups, Pure Appl. Math. 46, Academic Press, New York, 1972.
6. J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74.
7. J. Cheeger and D. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland Math. Library 9, North-Holland, Amsterdam, 1975.
8. J. Cheeger, K. Fukaya, and M. Gromov, Nilpotent structures and invariant metrics on collapsed manifolds, J. Amer. Math. Soc. 5 (1992), 327-372.
9. J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, I, J. Differential Geom. 23 (1986), 309-346.
10. J. Cheeger and M. Gromov, Collapsing Riemannian manifolds while keeping their curvature bounded, II, J. Differential Geom. 32 (1990), 269-298.
11. J. Cheeger and M. Gromov, “On the characteristic numbers of complete manifolds of bounded curvature and finite volume” in Differential Geometry and Complex Analysis, Springer-Verlag, Berlin, 1985, 115-154.
12. J. Cheeger and X. Rong, Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry, Geom. Funct. Anal. 5 (1995), 141-163.
13. J. Cheeger and X. Rong, Existence of polarized F-structures on collapsed manifolds with bounded curvature and diameter, Geom. Funct. Anal. 6 (1996), 411-429.
14. X. Dai, Z. Shen, and G. Wei, Negative Ricci curvature and isometry group, Duke Math. J. 76 (1994), 59-73.
15. X. Dai, G. Wei, and R. Ye, Smoothing Riemannian metrics with Ricci curvature bounds, Manuscripta Math. 90 (1996), 49-61.
16. K. Fukaya, Collapsing Riemannian manifolds to ones of lower dimensions, J. Differential Geom. 25 (1987), 139-156.
17. K. Fukaya, A boundary of the set of Riemannian manifolds with bounded curvatures and diameters, J. Differential Geom. 28 (1988), 1-21.
18. K. Fukaya, Collapsing Riemannian manifolds to ones with lower dimension, II, J. Math. Soc. Japan 41 (1989), 333-356.
19. K. Fukaya, “Hausdorff convergence of Riemannian manifolds and its applications” in Recent Topics in Differential and Analytic Geometry, Adv. Stud. Pure Math. 18-1, Academic Press, Boston, 1990, 143-238.
20. L. Z. Gao and S.-T. Yau, The existence of negatively Ricci curved metrics on three-manifolds, Invent. Math. 85 (1986), 637-652.
21. M. Gromov, Almost flat manifolds, J. Differential Geom. 13 (1978), 231-241.
22. M. Gromov, Manifolds of negative curvature, J. Differential Geom. 13 (1978), 223-230.
23. M. Gromov, Volume and bounded cohomology, Inst. Hautes Etudes Sci. Publ. Math. 56 (1983), 5-99.
24. K. Grove, “Metric and topological measurements of manifolds” in Proceedings of the International Congress of Mathematicans, Vols. 1, 2 (Kyoto, 1990), Math. Soc. Japan, Tokyo, 1991, 511-519.
25. K. Grove, P. Petersen, and J.-Y. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), 205-213; Erratum, Invent. Math. 104 (1991), 221-222.
26. R. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306.
27. S. Kobayashi, Transformation Groups in Differential Geometry, Ergeb. Math. Grenzgeb. 70, Springer-Verlag, Berlin, 1972.
28. J. Lohkamp, Metrics of negative Ricci curvature, Ann. of Math. (2) 140 (1994), 655-683.
29. M. Min-Oo, Almost Einstein manifolds of negative Ricci curvature, J. Differential Geom. 32 (1990), 457-472.
30. 2-curvature pinching, Comment. Math. Helv. 65 (1990), 36-51.
31. G. Perel’man, A. D. Aleksandrov spaces with curvatures bounded below, II, preprint.
32. P. Petersen, G. Wei, and R. Ye, Controlled geometry via smoothing, preprint, 1995.
33. X. Rong, Bounding homotopy and homology groups by curvature and diameter, Duke Math. J. 78 (1995), 427-435.
34. X. Rong, On the fundamental groups of manifolds of positive sectional curvature. Ann. of Math. (2) 143 (1996), 397-411.
35. Z. Shen, Deforming metrics with curvature and injectivity radius bounded from below, Arch. Math. (Basel) 62 (1994), 354-367.
36. W.-X. Shi, Deforming the metric on complete Riemannian manifolds, J. Differential Geom. 30 (1989), 223-301.