Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Integrability of an almost complex structure on $S^4\times_f V^2$

Jong Taek Cho, Sun Hyang Chun, Yunhee Euh

Chonnam National University; Chosun University; Chonnam National University

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.

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).