Some remarks on homogeneous Kähler manifolds

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 μ 0 ω , admits a holomorphic isometric immersion in the complex projective space,...

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Bibliographic Details
Published in:Geometriae dedicata 2015-12, Vol.179 (1), p.377-383
Main Authors: Loi, Andrea, Mossa, Roberto
Format: Article
Language:English
Subjects:
Algebraic Geometry
Convex and Discrete Geometry
Differential Geometry
Hyperbolic Geometry
Mathematics
Mathematics and Statistics
Original Paper
Projective Geometry
Topology
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Summary: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 μ 0 ω , admits a holomorphic isometric immersion in the complex projective space, for a suitable μ 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.
ISSN:0046-5755
1572-9168
DOI:10.1007/s10711-015-0085-5