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On the non-existence of common submanifolds of Kähler manifolds and complex space forms

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Abstract

Two Kähler manifolds are called relatives if they admit a common Kähler submanifold with their induced metrics. In this paper, we provide a sufficient condition to determine whether a real analytic Kähler manifold is not a relative to a complex space form equipped with its canonical metric. As an application, we show that minimal domains, bounded homogeneous domains and some Hartogs domains equipped with their Bergman metrics are not relatives to the complex Euclidean space.

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Acknowledgements

The authors would like to sincerely thank referees for their suggestions and comments, which greatly improve the exposition of the paper. This project was partially supported by NSF of China (Grant No. 11301215, 11601422, 11671270, 11871044), Natural Science Foundation of Shaanxi Province (2019JQ-398) and Scientific Research Program of Shaanxi Provincial Education Department (19JK0841).

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Correspondence to Yihong Hao.

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Cheng, X., Hao, Y. On the non-existence of common submanifolds of Kähler manifolds and complex space forms. Ann Glob Anal Geom 60, 167–180 (2021). https://doi.org/10.1007/s10455-021-09776-3

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