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Negatively Ricci curved manifolds
Author:
Joachim Lohkamp
Journal:
Bull. Amer. Math. Soc. 27 (1992), 288-291
MSC (2000):
Primary 53C21; Secondary 57R99
MathSciNet review:
1161276
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Abstract: In this paper we announce the following result: "Every manifold of dimension admits a complete negatively Ricci curved metric." Furthermore we describe some sharper results and sketch proofs.
- [A]
Thierry
Aubin, Métriques riemanniennes et courbure, J.
Differential Geometry 4 (1970), 383–424 (French). MR 0279731
(43 #5452)
- [BK]
John
Bland and Morris
Kalka, Negative scalar curvature metrics on
noncompact manifolds, Trans. Amer. Math.
Soc. 316 (1989), no. 2, 433–446. MR 987159
(90f:53072), http://dx.doi.org/10.1090/S0002-9947-1989-0987159-2
- [Bg]
Jean-Pierre
Bourguignon, Ricci curvature and Einstein metrics, Global
differential geometry and global analysis (Berlin, 1979) Lecture Notes in
Math., vol. 838, Springer, Berlin, 1981, pp. 42–63. MR 636265
(83c:53056)
- [Br1]
Robert
Brooks, A construction of metrics of negative Ricci curvature,
J. Differential Geom. 29 (1989), no. 1, 85–94.
MR 978077
(90c:53099)
- [G]
L.
Zhiyong Gao, The construction of negatively Ricci curved
manifolds, Math. Ann. 271 (1985), no. 2,
185–208. MR
783551 (86h:53044), http://dx.doi.org/10.1007/BF01455986
- [GY]
L.
Zhiyong Gao and S.-T.
Yau, The existence of negatively Ricci curved metrics on
three-manifolds, Invent. Math. 85 (1986), no. 3,
637–652. MR
848687 (87j:53061), http://dx.doi.org/10.1007/BF01390331
- [Gr]
Mikhael
Gromov, Structures métriques pour les variétés
riemanniennes, Textes Mathématiques [Mathematical Texts],
vol. 1, CEDIC, Paris, 1981 (French). Edited by J. Lafontaine and P.
Pansu. MR
682063 (85e:53051)
- [K]
Jerry
L. Kazdan, Prescribing the curvature of a Riemannian manifold,
CBMS Regional Conference Series in Mathematics, vol. 57, Published for
the Conference Board of the Mathematical Sciences, Washington, DC, 1985. MR 787227
(86h:53001)
- [T]
W. Thurston, The geometry and topology of three manifolds, Princeton Lecture Notes, vol. 57, Princeton, NJ, 1980.
- [Y]
Shing
Tung Yau, Problem section, Seminar on Differential Geometry,
Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, N.J.,
1982, pp. 669–706. MR 645762
(83e:53029)
- [A]
- T. Aubin, Métriques riemanniennes et courbure, J. Differential Geom. 4 (1970), 383-424. MR 0279731 (43:5452)
- [BK]
- J. Bland and M. Kalka, Negative scalar curvature metrics on noncompact manifolds, Trans. Amer. Math. Soc. 316 (1989), 433-446. MR 987159 (90f:53072)
- [Bg]
- J. P. Bourguignon, Ricci curvature and Einstein metrics, Global Differential Geometry, Lecture Notes in Math., vol. 838, Springer, New York, 1981, pp. 42-63. MR 636265 (83c:53056)
- [Br1]
- R. Brooks, A construction of metrics of negative Ricci curvature, J. Differential Geom. 29 (1989), 85-94. MR 978077 (90c:53099)
- [G]
- L. Z Gao, The construction of negatively Ricci curved manifolds, Math. Ann. 271 (1985), 185-208. MR 783551 (86h:53044)
- [GY]
- L. Z. Gao and S. T. Yau, The existence of negatively Ricci curved on three manifolds, Invent. Math. 85 (1986), 637-652. MR 848687 (87j:53061)
- [Gr]
- M. Gromov, Structures métriques pour les variétés riemanniennes, Editions CEDIC, Paris, 1981. MR 682063 (85e:53051)
- [K]
- J. L. Kazdan, Prescribing the curvature of a Riemannian manifold, CBMS Regional Conf. Ser. in Math., vol. 57, Conf. Board Math. Sci., Washington, DC, 1985. MR 787227 (86h:53001)
- [T]
- W. Thurston, The geometry and topology of three manifolds, Princeton Lecture Notes, vol. 57, Princeton, NJ, 1980.
- [Y]
- S. T. Yau, Seminar on differential geometry, problem section, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, Princeton, NJ, 1982. MR 645762 (83e:53029)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0273-0979-1992-00325-7
PII:
S 0273-0979(1992)00325-7
Article copyright:
© Copyright 1992 American Mathematical Society
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