Abstract
The authors generalize Cartan’s Lemma, a characterization of real space form, for any four orthonormal vector fields (instead of three) for an indefinite K-space.
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References
A. Gray, Nearly Kaehler Manifolds, J. Diff. Geom. 4, 283 (1970).
S. Sawaki, Y. Watanabe, and T. Sato, Notes on a K-Space of Constant Holomorphic Sectional Curvature, Kodai Math. Sem. Rep. 26, 438 (1975).
E. Cartan, Lecons Sur La Geometric des Espaces de Riemann (Paris Gauthier Villars, 1946).
L. Graves and K. Nomizu, On Sectional Curvature of Indefinite Metric I, Math. Ann. 232, 267 (1978).
M. Barros and A. Remero, Indefinite Kaehler Manifolds, Math. Ann. 266, 55 (1982).
R. K. Nagaich and S. I. Hussain, Constancy of Holomorphic Sectional Curvature in Pseudo-Kaehler Manifolds, Communication de la Faculte’des Sc. I. Univ. d’Ankara Serie AL, Tome 33, 137 (1984).
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submitted by M.A. Malakhaltsev
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Kumar, R., Nagaich, R.K. Generalization of Cartan’s Lemma for indefinite K-spaces. Lobachevskii J Math 29, 21–23 (2008). https://doi.org/10.1134/S1995080208010058
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DOI: https://doi.org/10.1134/S1995080208010058