대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제59권4호
  • /
  • Pages.801-810
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  • 2022
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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INTEGRABILITY OF AN ALMOST COMPLEX STRUCTURE ON S4 × fV2

  • Cho, Jong Taek (Department of Mathematics Chonnam National University) ;
  • Chun, Sun Hyang (Department of Mathematics Chosun University) ;
  • Euh, Yunhee (Department of Mathematics Chonnam National University)
  • 투고 : 2020.07.15
  • 심사 : 2022.05.09
  • 발행 : 2022.07.31
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초록

In this paper, we prove that any orthogonal almost complex structure on a warped product manifold of any oriented closed surface and a round 4-sphere for a concircular warping function on the sphere is never integrable. This gives a partial answer to Calabi's problem.

키워드

과제정보

The authors would like to thank the referee for carefully reading the manuscript and for valuable comments to improve it.

참고문헌

  1. R. L. Bishop and B. O'Neill, Manifolds of negative curvature, Trans. Amer. Math. Soc. 145 (1969), 1-49. https://doi.org/10.2307/1995057
  2. E. Calabi, Construction and properties of some 6-dimensional almost complex manifolds, Trans. Amer. Math. Soc. 87 (1958), 407-438. https://doi.org/10.2307/1993108
  3. B.-Y. Chen, Differential Geometry of Warped Product Manifolds and Submanifolds, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2017. https://doi.org/10.1142/10419
  4. Y. Euh and K. Sekigawa, Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres, J. Korean Math. Soc. 50 (2013), no. 2, 231-240. https://doi.org/10.4134/JKMS.2013.50.2.231
  5. Y. Euh and K. Sekigawa, Notes on a question raised by E. Calabi, Bull. Korean Math. Soc. 53 (2016), no. 1, 83-90. https://doi.org/10.4134/BKMS.2016.53.1.083
  6. A. Gray, Curvature identities for Hermitian and almost Hermitian manifolds, Tohoku Math. J. (2) 28 (1976), no. 4, 601-612. https://doi.org/10.2748/tmj/1178240746
  7. W. A. Sutherland, A note on almost complex and weakly complex structures, J. London Math. Soc. 40 (1965), 705-712. https://doi.org/10.1112/jlms/s1-40.1.705
  8. Y. Tashiro, Complete Riemannian manifolds and some vector fields, Trans. Amer. Math. Soc. 117 (1965), 251-275. https://doi.org/10.2307/1994206