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Regular Riemannian  -manifolds of noncompact type
Author:
Cristián U. Sánchez
Journal:
Proc. Amer. Math. Soc. 88 (1983), 110-112
MSC:
Primary 53C35; Secondary 53C42
MathSciNet review:
691288
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Abstract: In this note it is proven that a regular Riemannian  -manifold of noncompact type (see below) cannot be immersed isometrically and equivariantly in  .
- [1]
Alfred
Gray, Riemannian manifolds with geodesic symmetries of order
3, J. Differential Geometry 7 (1972), 343–369.
MR
0331281 (48 #9615)
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Sigurđur
Helgason, Differential geometry and symmetric spaces, Pure and
Applied Mathematics, Vol. XII, Academic Press, New York, 1962. MR 0145455
(26 #2986)
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Oldřich
Kowalski, Generalized symmetric spaces, Lecture Notes in
Mathematics, vol. 805, Springer-Verlag, Berlin, 1980. MR 579184
(83d:53036)
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V.
S. Varadarajan, Lie groups, Lie algebras, and their
representations, Prentice-Hall Inc., Englewood Cliffs, N.J., 1974.
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(51 #13113)
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Jorge
Vargas, A symmetric space of noncompact type
has no equivariant isometric immersions into the Euclidean space,
Proc. Amer. Math. Soc. 81 (1981),
no. 1, 149–150. MR 589158
(81j:53054), http://dx.doi.org/10.1090/S0002-9939-1981-0589158-X
- [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:
http://dx.doi.org/10.1090/S0002-9939-1983-0691288-0
PII:
S 0002-9939(1983)0691288-0
Keywords:
Regular  -manifold,
isometric equivariant immersion,
Levi decomposition,
 -symmetric space
Article copyright:
© Copyright 1983 American Mathematical Society
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