논문KCI 등재
Integrability of an almost complex structure on $S^4\times_f V^2$
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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.
Abstract
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.
참고문헌 (8)
- R. L. Bishop, "Manifolds of negative curvature", Trans. Amer. Math. Soc, 145, pp.1~49 (1969)[DOI]
- E. Calabi, "Construction and properties of some 6-dimensional almost complex manifolds", Trans. Amer. Math. Soc, 87, pp.407~438 (1958)[DOI]
- B. -Y. Chen, "Differential Geometry of Warped Product Manifolds and Submanifolds" (2017), World Scientific Publishing Co. Pte. Ltd
- 어은희, "Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres", 대한수학회지, 50(2), pp.231~240 (2013), 대한수학회
- Yunhee Euh, "Notes on a question raised by E. Calabi", 대한수학회보, 53(1), pp.83~90 (2016), 대한수학회
- Alfred Gray, "Curvature identities for Hermitian and almost Hermitian manifolds", Tohoku Mathematical Journal, 28(4) (1976), Mathematical Institute, Tohoku University[DOI]
- W. A. Sutherland, "A note on almost complex and weakly complex structures", J. London Math. Soc, 40, pp.705~712 (1965)[DOI]
- Y. Tashiro, "Complete Riemannian manifolds and some vector fields", Trans. Amer. Math. Soc, 117, pp.251~275 (1965)[DOI]
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