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On isotropy irreducible Riemannian manifolds

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References

  • [BB]Berard Bergery, L., Les variétés Riemanniennes homogènes simplement connexes de dimension impair a courbure strictement positive.J. Math. Pures Appl., 55 (1976), 47–68.

    MATH  MathSciNet  Google Scholar 

  • [Be]Besse, A.,Einstein Manifolds. Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, Band 10. Springer-Verlag, 1987.

  • [Bl]Bleecker, D. D., Critical Riemannian manifolds.J. Differential Geom., 14 (1979), 599–608.

    MATH  MathSciNet  Google Scholar 

  • [C 1]Cartan, E., Sur une classe remarquable d'espaces de Riemann.Bull. Soc. Math France, 54 (1926), 214–264; 55 (1927), 114–134.

    MATH  MathSciNet  Google Scholar 

  • [C 2]Cartan, E., Sur la structure des groupes de transformations finis, et continus. Thèse, Paris (1894).

  • [CCNPW]Conway, J., Curtis, R., Norton, S., Parker, R. &Wilson, R.,Atlas of Finite Groups. Clarenden Press, Oxford, 1985.

    MATH  Google Scholar 

  • [Fr 1]Freudenthal, H., Sur le groupe exceptionnel E7.Nederl. Akad. Wetensch. Proc. Ser. A, 56 (1953), 81–89.

    MATH  MathSciNet  Google Scholar 

  • [Fr 2]-—, Beziehungen der E7 und E8 zur Oktavenebene I.Nederl. Akad. Wetensch. Proc. Ser. A, 57, (1954), 218–230.

    MATH  MathSciNet  Google Scholar 

  • [Go]Golubitsky, M., Primitive actions and maximal subgroups of Lie groups.J. Differential Geom., 7 (1972), 175–191.

    MATH  MathSciNet  Google Scholar 

  • [GR]Golubitsky, M. &Rotschild, B., Primitive subalgebras of exceptional Lie algebras.Bull. Math. Soc., 77 (1971), 983–986.

    Article  MATH  Google Scholar 

  • [KN]Kobayashi, S. &Nomizu, K.,Foundations of Differential Geometry, Vol 2. Interscience, N.Y., 1969.

    MATH  Google Scholar 

  • [K]Krämer, M., Eine Klassifikation bestimmter, Untergruppen kompakter zusammenhängender Liegruppen.Comm. Algebra, 3 (1975), 691–737.

    MATH  MathSciNet  Google Scholar 

  • [L]Li, P., Minimal immersions of compact irreducible homogeneous Riemannian manifolds.J. Differential Geom., 16 (1981), 105–115.

    MATH  MathSciNet  Google Scholar 

  • [Ma 1]Manturov, O. V., Homogeneous asymmetric Riemannian spaces with an irreducible group of motions.Dokl. Akad. Nauk SSSR, 141 (1961), 792–795.

    MATH  MathSciNet  Google Scholar 

  • [Ma 2]-—, Riemannian spaces with orthogonal and symplectic groups of motions and an irreducible group of rotations.Dokl. Akad. Nauk. SSSR, 141 (1961), 1034–1037.

    MATH  MathSciNet  Google Scholar 

  • [Ma 3]-—, Homogeneous Riemannian manifolds with irreducible isotropy group.Trudy Sem. Vector. Tenzor. Anal., 13 (1966), 68–145.

    MATH  MathSciNet  Google Scholar 

  • [O]Oniščik, A. L., On transitive compact transformation groups.Amer. Math. Soc. Transl. Ser. 2, 55 (1966), 153–194.

    Google Scholar 

  • [TT]Takagi, R. & Takahashi, T., On the principal curvatures of homogeneous hypersurfaces in a sphere.Differential Geometry in honor of K. Yano, Tokyo (1972), 469–481.

  • [Ta]Takahashi, T., Minimal immersions of Riemannian manifolds.J. Math. Soc. Japan, 18 (1966), 380–385.

    Article  MATH  MathSciNet  Google Scholar 

  • [Wa]Wallach, N. R., Compact homogeneous Riemannian manifords with, strictly positive curvature.Ann. of Math., 96 (1972), 277–295.

    Article  MATH  MathSciNet  Google Scholar 

  • [WZ 1]Wang, M. &Ziller, W., On normal homogeneous Einstein manifolds.Ann. Sci. École Norm. Sup. (4), 18 (1985), 563–633.

    MATH  MathSciNet  Google Scholar 

  • [WZ 2]Wang, M. & Ziller, W., Symmetric spaces and strongly isotropy irreducible spaces. Preprint (1990).

  • [Wo 1]Wolf, J. A., The geometry and structure of isotropy irreducible homogeneous spaces.Acta Math., 120 (1968), 59–148; correction,Acta Math., 152 (1984), 141–142.

    Article  MATH  MathSciNet  Google Scholar 

  • [Wo 2]Wolf, J. A.,Spaces of Constant Curvature. 4th edition, Publish or Perish Inc., 1977.

  • [WG]Wolf, J., &Gray, A., Homogeneous spaces defined by Lie group automorphisms I.J. Differential Geom., 2 (1968), 77–114.

    MATH  MathSciNet  Google Scholar 

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The first author acknowledges partial support from the Natural Sciences and Engineering Research Council of Canada.

The second author acknowledges partial support from the National Science Foundation.

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Wang, M., Ziller, W. On isotropy irreducible Riemannian manifolds. Acta Math 166, 223–261 (1991). https://doi.org/10.1007/BF02398887

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  • DOI: https://doi.org/10.1007/BF02398887

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