A bounded homogeneous domain and a projective manifold are not relatives

Abstract

Let $M_1$ and $M_2$ be two Kähler manifolds. One says that $M_1$ and $M_2$ are "relatives" if they share a non-trivial Kähler submanifold $S$, namely, if there exist two holomorphic and isometric immersions (Kähler immersions) $h_1:S->M_1$ and $h_2:S->M_2$. In this paper we show that a bounded homogeneous domain with a homogeneous Kähler metric and a projective Kähler manifold (i.e. a projective manifold endowed with the restriction of the Fubini-Study metric) are not relatives. Our result is a generalization of the result obtained by A. J. Di Scala and A. Loi (in "Kähler manifolds and their relatives", Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 9 3 (2010), 495-501) for the Bergman metrics.

5 pages. arXiv admin note: text overlap with arXiv:math/0601739 by other authors

References in corpus (1)

• Berezin quantization of homogeneous bounded domains

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