Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T00:30:26.889Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Barros, M., Montiel, S. and Romero, A. The topology of indefinite flag manifolds. (Preprint.)Google Scholar
(2)Barros, M. and Romero, A.Indefinite Kählerian manifolds. Math. Ann. 261 (1982), 55–62.CrossRefGoogle Scholar
(3)Kobayashi, S. and Nomizu, K.Foundations of differential geometry. Interscience (1963, 1969).Google Scholar
(4)Kulkarni, R. S.The values of sectional curvature in indefinite metrics. Comm. Math. Helv. 54 (1974), 173–176.CrossRefGoogle Scholar
(5)Wolf, J. A.Spaces of constant curvature (McGraw-Hill, 1967).Google Scholar
(6)Wong, Y. C.Sectional curvatures of Grassmann manifolds. Proc. Nat. Acad. Sci. 60 (1968), 75–79.CrossRefGoogle ScholarPubMed