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Regular Riemannian $ s$-manifolds of noncompact type


Author: Cristián U. Sánchez
Journal: Proc. Amer. Math. Soc. 88 (1983), 110-112
MSC: Primary 53C35; Secondary 53C42
DOI: https://doi.org/10.1090/S0002-9939-1983-0691288-0
MathSciNet review: 691288
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Abstract: In this note it is proven that a regular Riemannian $ s$-manifold of noncompact type (see below) cannot be immersed isometrically and equivariantly in $ {R^n}$.


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

  • [1] A. Gray, Riemannian manifolds with geodesic symmetries of order 3, J. Differential Geom. 7 (1972), 343-369. MR 0331281 (48:9615)
  • [2] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York and London, 1962. MR 0145455 (26:2986)
  • [3] O. Kowalski, Generalized symmetric spaces, Lecture Notes in Math., vol. 805, Springer-Verlag, Berlin and New York, 1980. MR 579184 (83d:53036)
  • [4] V. S. Varadarajan, Lie groups, Lie algebras and their representations, Prentice-Hall, Englewood Cliffs, N. J., 1974. MR 0376938 (51:13113)
  • [5] J. Vargas, A symmetric space of noncompact type has no equivariant isometric immersion into Euclidean space, Proc. Amer. Math. Soc. 81 (1981), 149-150. MR 589158 (81j:53054)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0691288-0
Keywords: Regular $ s$-manifold, isometric equivariant immersion, Levi decomposition, $ 3$-symmetric space
Article copyright: © Copyright 1983 American Mathematical Society

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