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Proceedings of the American Mathematical Society

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Naturally reductive metrics of nonpositive Ricci curvature


Authors: Carolyn Gordon and Wolfgang Ziller
Journal: Proc. Amer. Math. Soc. 91 (1984), 287-290
MSC: Primary 53C30; Secondary 53C25
DOI: https://doi.org/10.1090/S0002-9939-1984-0740188-7
MathSciNet review: 740188
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Abstract | References | Similar Articles | Additional Information

Abstract: The main theorem states that every naturally reductive homogeneous Riemannian manifold of nonpositive Ricci curvature is symmetric. As a corollary, every noncompact naturally reductive Einstein manifold is symmetric.


References [Enhancements On Off] (What's this?)

  • [DZ] J. D'Atri and W. Ziller, Naturally reductive metrics and Einstein metrics on compact Lie groups, Mem. Amer. Math. Soc., No. 215 (1979). MR 519928 (80i:53023)
  • [D] E. D. Deloff, Naturally reductive metrics and metrics with volume preserving geodesic symmetries on NC algebras, Thesis, Rutgers, 1979.
  • [G] C. Gordon, Naturally reductive Riemannian manifolds, preprint 1984.
  • [G-W] C. Gordon and E. N. Wilson, The fine structure of transitive Riemannian isometry groups. I, preprint 1984. MR 779070 (86g:53056)
  • [H] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [K] S. Kobayashi, Transformation groups in differential geometry, Springer-Verlag, Berlin and New York, 1972. MR 0355886 (50:8360)
  • [LM] M. L. Leite and I. D. Miatello, Metrics of negative Ricci curvature on $ {\text{SL}}(n,{\mathbf{R}})$, $ n \geqslant 3$, J. Differential Geom. 17 (1982), 635-641. MR 683168 (84c:53049)
  • [M] J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 243-329. MR 0425012 (54:12970)
  • [WZ] M. Wang and W. Ziller, On normal homogeneous Einstein metrics, preprint 1984. MR 757214 (85m:53052)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0740188-7
Article copyright: © Copyright 1984 American Mathematical Society

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