Proceedings of the American Mathematical Society

Author(s): Dezhong Chen
Journal: Proc. Amer. Math. Soc. 137 (2009), 273-278.
MSC (2000): Primary 53C21
Posted: August 4, 2008
Retrieve article in: PDF

Abstract: We show that only two types of Ricci signatures cannot be realized by any left-invariant metric on 4-dimensional Lie groups.

1.: D. M. DeTurck, Existence of metrics with prescribed Ricci curvature: local theory, Invent. Math. 65 (1981/82), no. 1, 179-207. MR 636886 (83b:53019)
2.: I. Dotti-Miatello, Ricci curvature of left invariant metrics on solvable unimodular Lie groups, Math. Z. 180 (1982), no. 2, 257-263. MR 661702 (84a:53044)
3.: J. Isenberg, M. Jackson, P. Lu, Ricci flow on locally homogeneous closed -manifolds, Comm. Anal. Geom. 14 (2006), no. 2, 345-386. MR 2255014 (2007e:53087)
4.: G. R. Jensen, Homogeneous Einstein spaces of dimension four, J. Differential Geometry 3 (1969), 309-349. MR 0261487 (41:6100)
5.: J. Lohkamp, Metrics of negative Ricci curvature, Ann. of Math. (2) 140 (1994), no. 3, 655-683. MR 1307899 (95i:53042)
6.: M. A. H. MacCallum, On the classification of the real four-dimensional Lie algebras, On Einstein's path (A. Harvey, ed.), Springer, New York, 1999, pp. 299-317. MR 1658911 (99k:17010)
7.: J. Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293-329. MR 0425012 (54:12970)
8.: J. Patera, R. T. Sharp, P. Winternitz, H. Zassenhaus, Invariants of real low dimension Lie algebras, J. Mathematical Phys. 17 (1976), no. 6, 986-994. MR 0404362 (53:8164)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 53C21

Dezhong Chen
Affiliation: Department of Mathematics \& Statistics, McMaster University, Hamilton, Ontario L8S 4K1, Canada
Email: chend6@math.mcmaster.ca

DOI: 10.1090/S0002-9939-08-09572-5
PII: S 0002-9939(08)09572-5
Keywords: Left-invariant metric, Ricci signature
Received by editor(s): December 18, 2007
Posted: August 4, 2008
Communicated by: Jon G. Wolfson
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS