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Holomorphic sectional curvatures of indefinite complex Grassmann manifolds

Published online by Cambridge University Press:  24 October 2008

Sebastian Montiel  and
Alfonso Romero
Sebastian Montiel
Affiliation:
University of Granada, Spain
Alfonso Romero
Affiliation:
University of Granada, Spain
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Extract

In (2), indefinite Kählerian manifolds have been examined from the point of view of holomorphic sectional curvature. Examples in (2) show that the analogue of Kulkarni's theorem (see (4), p. 173) for the holomorphic sectional curvature is false and the best possible result in the direction is:

Theorem 1 (known, (2)). Let M be a connected indefinite Kählerian manifold with complex dimension n ≥ 2. If the holomorphic sectional curvature of M is bounded above and bounded below, then M is an indefinite complex space form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 93 , Issue 1 , January 1983 , pp. 121 - 125
Copyright
Copyright © Cambridge Philosophical Society 1983

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References

REFERENCES

(1)Barros, M., Montiel, S. and Romero, A. The topology of indefinite flag manifolds. (Preprint.)Google Scholar
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