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Zbl 0765.53051
Bonome, Agustín; Castro, Regina; García-Río, Eduardo; Hervella, Luis M.
On the holomorphic sectional curvature on an indefinite Kähler manifold. (English. Abridged French version)
[J] C. R. Acad. Sci., Paris, Sér. I 315, No.11, 1183-1187 (1992). ISSN 0764-4442

Summary: It is shown that for a general indefinite almost Hermitian manifold boundedness on the holomorphic sectional curvature leads to spaces of pointwise constant holomorphic sectional curvature. A family of null holomorphically flat indefinite Kähler manifolds but not of constant holomorphic sectional curvature is exhibited. Finally, we provide two criteria for the constancy of the holomorphic sectional curvature.

MSC 2000:: *53C55 Complex differential geometry (global)
53C50 Lorentz manifolds, manifolds with indefinite metrics
53C15 Geometric structures on manifolds

Keywords: indefinite almost Hermitian manifold; constant holomorphic sectional curvature; indefinite Kähler manifolds

Cited in: Zbl 0853.53028 Zbl 0836.53021

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