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Notes on a question raised by E. Calabi
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We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.
Abstract
We show that any orthogonal almost complex structure on a warped product Riemannian manifold of an oriented closed surface with nonnegative Gaussian curvature and a round 4-sphere is never integrable. This provides a partial answer to a question raised by E. Calabi.
참고문헌 (7)
- R. L. Bishop, "Manifolds of negative curvature", Trans. Amer. Math. Soc, 145, pp.1~49 (1969)
- E. Calabi, "Construction and properties of some 6-dimensional almost complex manifold", Trans. Amer. Math. Soc, 87, pp.407~438 (1958)
- 어은희, "Orthogonal almost complex structures on the Riemannian products of even-dimensional round spheres", 대한수학회지, 50(2), pp.231~240 (2013), 대한수학회
- A. Gray, "Curvature identities for Hermitian and almost Hermitian manifolds", Tohoku Math, 28(4), pp.601~612 (1976)
- S. Salamon, "Harmonic and holomorphic maps, Geometry Seminar, “Luigi Bianchi” II–1984", Lecture Notes in Math, 1164, pp.161~224 (1985), Springer-Verlag
- K. Sekigawa, "Almost Hermitian structures on twistor bundles", Proceedings of the Ra-manujan Centennial International Conference, pp.127~136 (1988), Ramanujan Math. Soc.
- W. A. Sutherland, "A note on almost complex and weakly complex structures", J. London Math. Soc, 40, pp.705~712 (1965)
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