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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost Hermitian structures induced from a Kähler structure which has constant holomorphic sectional curvature


Author: Takuji Sato
Journal: Proc. Amer. Math. Soc. 131 (2003), 2903-2909
MSC (2000): Primary 53B35, 53C15, 53C55
Published electronically: April 9, 2003
MathSciNet review: 1974348
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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain a non-Kähler almost Hermitian manifold of constant holomorphic sectional curvature by changing the almost complex structure in a Kähler manifold of constant holomorphic sectional curvature.


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  • 1. A. Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tôhoku Math. J., 28(1976), 601-612. MR 55:9005
  • 2. A. Gray and L. Vanhecke, Almost Hermitian manifolds with constant holomorphic sectional curvature, Casopis pro pestovánímat., 104(1979), 170-179. MR 80f:53039
  • 3. P. Nurowski and M. Przanowski, A four-dimensional example of a Ricci-flat metric admitting almost-Kähler non-Kähler structure, Classical Quantum Gravity, 16(1999), L9-L13. MR 2000a:53073
  • 4. S. Kobayashi and K. Nomizu, Foundations of differential geometry, I, II, Interscience Publishers, New York, 1963, 1969. MR 27:2945; MR 38:6501
  • 5. T. Sato, On some almost Hermitian manifolds with constant holomorphic sectional curvature, Kyungpook Math. J., 29(1989), 11-25. MR 91d:53052
  • 6. T. Sato, Some remarks on almost Kähler 4-manifolds of pointwise constant holomorphic sectional curvature, Kodai Math. J., 22(1999), 286-303. MR 2001c:53037
  • 7. T. Sato, An example of an almost Kähler manifold with pointwise constant holomorphic sectional curvature, Tokyo J. Math., 23(2000), 387-401. MR 2002b:53067
  • 8. T. Sato, Some examples of almost Kähler 4-manifolds, Balkan J. Geom. Appl., 5(2000), 113-137. MR 2003c:53059
  • 9. F. Tricerri and L. Vanhecke, Curvature tensors on almost Hermitian manifolds, Trans. Amer. Math. Soc., 267(1981), 365-398. MR 82j:53071

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Additional Information

Takuji Sato
Affiliation: Faculty of Engineering, Kanazawa University, Kanazawa, Japan
Email: tsato@t.kanazawa-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07132-6
PII: S 0002-9939(03)07132-6
Keywords: Almost Hermitian manifold, holomorphic sectional curvature
Received by editor(s): March 15, 2001
Published electronically: April 9, 2003
Communicated by: Mohan Ramachandran
Article copyright: © Copyright 2003 American Mathematical Society