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Some remarks on homogeneous Kähler manifolds

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Abstract

In this paper we provide a positive answer to a conjecture due to Di Scala et al. (Asian J Math, 2012, Conjecture 1) claiming that a simply-connected homogeneous Kähler manifold M endowed with an integral Kähler form \(\mu _0\omega \), admits a holomorphic isometric immersion in the complex projective space, for a suitable \(\mu _0>0\). This result has two corollaries which extend to homogeneous Kähler manifolds the results obtained by the authors Loi and Mossa (Geom Dedicata 161:119–128, 2012) and Mossa (J Geom Phys 86:492–496, 2014) for homogeneous bounded domains.

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Notes

  1. The authors thanks Hishi Hideyuki for reporting this result.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124, Cagliari, Italy

    Andrea Loi & Roberto Mossa

Authors
  1. Andrea Loi
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  2. Roberto Mossa
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Correspondence to Andrea Loi.

Additional information

The authors were supported by Prin 2010/11—Varietà reali e complesse: geometria, topologia e analisi armonica—Italy and also by INdAM. GNSAGA—Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni.

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Loi, A., Mossa, R. Some remarks on homogeneous Kähler manifolds. Geom Dedicata 179, 377–383 (2015). https://doi.org/10.1007/s10711-015-0085-5

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  • DOI: https://doi.org/10.1007/s10711-015-0085-5

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