Bull. Korean Math. Soc. 2022; 59(4): 801-810
Published online July 31, 2022 https://doi.org/10.4134/BKMS.b200606
Copyright © The Korean Mathematical Society.
Jong Taek Cho, Sun Hyang Chun, Yunhee Euh
Chonnam National University; Chosun University; Chonnam National University
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.
Keywords: Orthogonal complex structure, warped product, concircular function
MSC numbers: 53C15, 53C21, 53C55
Supported by: This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2019R1F1A1040829). S. H. Chun was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2018R1D1A1B07045729).
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