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Naturally reductive metrics of nonpositive Ricci curvature. (English) Zbl 0513.53049


MSC:

53C30 Differential geometry of homogeneous manifolds
53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.)
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[1] J. E. D’Atri and W. Ziller, Naturally reductive metrics and Einstein metrics on compact Lie groups, Mem. Amer. Math. Soc. 18 (1979), no. 215, iii+72. · Zbl 0404.53044
[2] E. D. Deloff, Naturally reductive metrics and metrics with volume preserving geodesic symmetries on NC algebras, Thesis, Rutgers, 1979.
[3] C. Gordon, Naturally reductive Riemannian manifolds, preprint 1984.
[4] Carolyn S. Gordon and Edward N. Wilson, The fine structure of transitive Riemannian isometry groups. I, Trans. Amer. Math. Soc. 289 (1985), no. 1, 367 – 380. · Zbl 0565.53030
[5] SigurĂ„’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[6] Shoshichi Kobayashi, Transformation groups in differential geometry, Springer-Verlag, New York-Heidelberg, 1972. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 70. · Zbl 0246.53031
[7] M. L. Leite and I. Dotti de Miatello, Metrics of negative Ricci curvature on \?\?(\?,\?), \?\ge 3, J. Differential Geom. 17 (1982), no. 4, 635 – 641 (1983). · Zbl 0482.53037
[8] John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293 – 329. · Zbl 0341.53030
[9] Wolfgang Ziller, Homogeneous Einstein metrics, Global Riemannian geometry (Durham, 1983) Ellis Horwood Ser. Math. Appl., Horwood, Chichester, 1984, pp. 126 – 135. · Zbl 0615.53038
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