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The index number of an  -space: An extension of a result of M.Takeuchi's
Author(s):
Cristián
U.
Sánchez
Journal:
Proc. Amer. Math. Soc.
125
(1997),
893-900.
MSC (1991):
Primary 53C30;
Secondary 53C35
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Abstract:
M. Takeuchi proved the following nice result: The ``two-number'' of a symmetric  -space is equal to the sum of the Betti numbers of the space with coefficients in  . In the present paper an extension of this result is given for general  -spaces.
References:
- [B]
- R. Bott, An application of the Morse theory to the topology of Lie groups, Bull. Soc. Math. France 84 (1956), 251-281. MR 19:291a
- [Ch-N]
- B. Y. Chen and T. Nagano, A Riemannian geometric invariant and its applications to a problem of Borel and Serre, Trans. Amer. Math. Soc. 308 (1988), 273-297. MR 89j:53046
- [F]
- D. Ferus, Symmetric submanifolds of Euclidean space, Math. Ann. 247 (1980), 81-93. MR 81i:53040
- [H]
- S. Helgason, Differential geometry, Lie groups and symmetric spaces, Academic Press, New York, 1978. MR 80k:53081
- [J]
- J. A. Jimenez, Existence of Hermitian
 -symmetric spaces and of noncommutative naturally reductive spaces, Math. Z. 196 (1987), 133-139. MR 89b:53088a - [K]
- O. Kowalski, Generalized symmetric spaces, Lecture Notes in Math., vol. 805, Springer, Berlin, Heidelberg, and New York, 1980. MR 83d:53036
- [M]
- I. G. Macdonald, Algebraic structure of Lie groups, Representation Theory of Lie Groups, London Math. Soc. Lecture Note Ser., vol. 34, Cambridge University Press, 1979, pp. 91-150. MR 81j:22001
- [S]
- C. U. Sanchez, The invariant of Chen-Nagano on flag manifolds, Proc. Amer. Math. Soc. 118 (1993), 1237-1242. MR 93j:53066
- [S1]
- C. U. Sanchez, The tightness of certain almost complex submanifolds, Proc. Amer. Math. Soc. 110 (1990), 807-811. MR 91b:53070
- [T]
- M. Takeuchi, Two-number of symmetric
 -spaces, Nagoya Math J. 115 (1989), 43-46. MR 90i:53066 - [T-K]
- M. Takeuchi and S. Kobayashi, Minimal imbeddings of
 -spaces, J. Differential Geometry 2 (1968), 203-215. MR 39:366 - [W]
- J. Wolf, The action of a real semisimple group on a complex flag manifold I: Orbit structure and holomorphic arc components, Bull. Amer. Math. Soc. 75 (1969), 1121-1237. MR 40:4477
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Additional Information:
Cristián
U.
Sánchez
Affiliation:
Fa. M.A.F., Universidad de Córdoba, Ciudad Universitaria, 5000, Córdoba, Argentina
Email:
csanchez@mate.uncor.edu
DOI:
10.1090/S0002-9939-97-03517-X
PII:
S 0002-9939(97)03517-X
Received by editor(s):
August 5, 1994
Received by editor(s) in revised form:
June 12, 1995
Additional Notes:
The author's research was partially supported by CONICET and CONICOR, Argentina
Communicated by:
Roe W. Goodman
Copyright of article:
Copyright
1997,
American Mathematical Society
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