Scalar curvature of Lie groups
HTML articles powered by AMS MathViewer
- by Hêng Lung Lai and Huei Shyong Lue PDF
- Proc. Amer. Math. Soc. 81 (1981), 311-315 Request permission
Abstract:
In this paper, we prove the following theorem: If $G$ is a connected Lie group, then $G$ admits left invariant metric of positive scalar curvature if and only if the universal covering space $\tilde G$ of $G$ is not homeomorphic to the Euclidean space.References
- Thierry Aubin, Métriques riemanniennes et courbure, J. Differential Geometry 4 (1970), 383–424 (French). MR 279731
- Halldór I. Elíasson, On variations of metrics, Math. Scand. 29 (1971), 317–327 (1972). MR 312427, DOI 10.7146/math.scand.a-11058
- Morikuni Goto, Lattices of subalgebras of real Lie algebras, J. Algebra 11 (1969), 6–24. MR 232894, DOI 10.1016/0021-8693(69)90098-2
- Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces, Pure and Applied Mathematics, vol. 80, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1978. MR 514561
- Nigel Hitchin, Harmonic spinors, Advances in Math. 14 (1974), 1–55. MR 358873, DOI 10.1016/0001-8708(74)90021-8
- John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 425012, DOI 10.1016/S0001-8708(76)80002-3
- R. Schoen and Shing Tung Yau, Existence of incompressible minimal surfaces and the topology of three-dimensional manifolds with nonnegative scalar curvature, Ann. of Math. (2) 110 (1979), no. 1, 127–142. MR 541332, DOI 10.2307/1971247
- Hidehiko Yamabe, On a deformation of Riemannian structures on compact manifolds, Osaka Math. J. 12 (1960), 21–37. MR 125546
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 81 (1981), 311-315
- MSC: Primary 53C20; Secondary 22E15
- DOI: https://doi.org/10.1090/S0002-9939-1981-0593479-4
- MathSciNet review: 593479