Submanifolds of some Hartogs domain and the complex Euclidean space

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 Cheng and Hao [On the non-existence of common submanifolds of Kahler manifolds and complex space forms. Ann Glob Anal Geom. 2021;60(1):167-180] and Cheng X, Niu Y. Submanifolds of Cartan-Hartogs domains and complex Euclidean spaces. J Math Anal Appl 2017;452(2):1262-1268.] and the novelty here is that the Bergman kernel of the Hartogs domain is not necessarily Nash algebraic.