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arXiv · 2206.02172

Submanifolds of some Hartogs domain and the complex Euclidean space

Xu Zhang·Donghai Ji
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Abstract

Two Kahler manifolds are called relatives if they admit a common Kahler submanifold with the same induced metrics. In this paper, we show that a Hartogs domain over an irreducible bounded symmetric domain equipped with the Bergman metric is not a relative to the complex Euclidean space. This generalizes the results in [5, 4] and the novelty here is that the Bergman kernel of the Hartogs domain is not necessarily Nash algebraic.

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Xu Zhang, Donghai Ji. 2022-06-05. Submanifolds of some Hartogs domain and the complex Euclidean space. https://doi.org/10.1080/17476933.2022.2084538

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