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Compact Hermitian surfaces of pointwise constant holomorphic sectional curvature

Published online by Cambridge University Press:  18 May 2009

Kouei Sekigawa  and
Takashi Koda
Kouei Sekigawa
Affiliation:
Department of Mathematics, Faculty of ScienceNiigata University, Niigata 950-21, Japan
Takashi Koda
Affiliation:
Department of Mathematics, Faculty of Science, Toyama University, Gofuku, Toyama 930, Japan E-mail address: [email protected] (Takashi Koda)
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Let M = (M, J, g) be an almost Hermitian manifold and U(M)the unit tangent bundle of M. Then the holomorphic sectional curvature H = H(x) can be regarded as a differentiable function on U(M). If the function H is constant along each fibre, then M is called a space of pointwise constant holomorphic sectional curvature. Especially, if H is constant on the whole U(M), then M is called a space of constant holomorphic sectional curvature. An almost Hermitian manifold with an integrable almost complex structure is called a Hermitian manifold. A real 4-dimensional Hermitian manifold is called a Hermitian surface. Hermitian surfaces of pointwise constant holomorphic sectional curvature have been studied by several authors (cf. [2], [3], [5], [6] and so on).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 37 , Issue 3 , September 1995 , pp. 343 - 349
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

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