Asian Journal of Mathematics

Volume 16 (2012)

Number 3

Kähler immersions of homogeneous Kähler manifolds into complex space forms

Pages: 479 – 487

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n3.a7

Authors

Antonio Jose di Scalia (Politecnico di Torino)

Hideyuki Ishi (Nagoya University)

Andrea Loi (Università di Cagliari)

Abstract

In this paper we study the homogeneous Kähler manifolds (h.K.m.) which can be Kähler immersed into finite or infinite dimensional complex space forms. On the one hand we completely classify the h.K.m. which can be Kähler immersed into a finite or infinite dimensional complex Euclidean or hyperbolic space. On the other hand, we extend known results about Kähler immersions into the finite dimensional complex projective space to the infinite dimensional setting. Key words. Kähler metrics, infinite dimensional complex space forms, homogeneous space, Wallach set.

Keywords

Kähler metrics, infinite dimensional complex space forms, homogeneous space, Wallach set

2010 Mathematics Subject Classification

53C55, 53D05, 58-xx

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