Notes on a question raised by E. Calabi
Bull. Korean Math. Soc. 2016 Vol. 53, No. 1, 83-90
Printed January 31, 2016
Yunhee Euh and Kouei Sekigawa
National Institute for Mathematical Sciences, Niigata University
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.
Keywords : orthogonal complex structure, warped product, curvature identity
MSC numbers : 53C15, 53C21, 53C55
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