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On 4-dimensional generalized complex space forms

Part of: Global differential geometry Local differential geometry

Published online by Cambridge University Press:  09 April 2009

Un Kyu Kim
Un Kyu Kim
Affiliation:
Department of Mathematics Education, Sung Kyun Kywan University, Seoul 110-745, Korea e-mail: [email protected]
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Abstract

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We characterize four-dimensional generalized complex forms and construct an Einstein and weakly *-Einstein Hermitian manifold with pointwise constant holomorphic sectional curvature which is not globally constant.

Keywords

generalized complex space formalmost Hermitian manifoldpointwise constant holomorphic sectional curvatureweakly *-Einstein

MSC classification

Secondary: 53C55: Hermitian and Kählerian manifolds 53B20: Local Riemannian geometry
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 66 , Issue 3 , June 1999 , pp. 379 - 387
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Derdzinski, A., ‘Exemples de métriques de Kahler et d'Einstein auto-duales sur le plan complexe’, in: Géométrie Riemannienne en Dimension 4. Séminaire Arthur Besse 1978/79 (Cedic/Fernand Nathan, Paris, 1981) pp. 334–346.Google Scholar
[2]Gray, A. and Vanhecke, L., ‘Almost Hermitian manifolds with constant holomorphic sectional curvature’, Časopis Pěst. Math. 104 (1979), 170–179.CrossRefGoogle Scholar
[3]Kim, U. K. and Jun, J.-B., ‘On 4-dimensional almost Hermitian manifolds with pointwise constant holomorphic sectional curvature’, Kyungpook Math. J. 35 (1996), 649–656.Google Scholar
[4]Kim, U. K., Kim, I. B. and Jun, J.-B., ‘On self-dual almost Hermitian 4-manifolds’, Nihonkai Math. J. 3 (1992), 163–176.Google Scholar
[5]Olszak, Z., ‘On the existence of generalized complex space forms’, Israel J. Math. 65 (1989), 214–218.Google Scholar
[6]Sato, T., ‘On some almost Hermitian manifolds with constant holomorphic sectional curvature’, Kyungpook Math. J. 29 (1989), 11–25.Google Scholar
[7]Sekigawa, K., ‘Geometry of almost Hermitian manifold’, in: Proceedings of the Topology and Geometry Research Center 5 (12. 1994) pp. 73–153.Google Scholar
[8]Tricerri, F. and Vanhecke, L., ‘Curvature tensors on almost Hermitian manifolds’, Trans. Amer. Math. Soc. 267 (1981), 365–398.CrossRefGoogle Scholar
[9]Yano, K., Differential geometry on complex and almost complex spaces (Pergamon Press, New York, 1965).Google Scholar
[10]Yano, K. and Kon, M., Structures on manifolds, Ser. Pure Math. 3 (World Scientific Publ., Singapore, 1984).Google Scholar