Asian Journal of Mathematics

Kähler Immersions of Homogeneous Kähler Manifolds into Complex Space Forms

Antonio Jose Di Scala, Hideyuki Ishi, and Andrea Loi

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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.

Article information

Source
Asian J. Math., Volume 16, Number 3 (2012), 479-488.

Dates
First available in Project Euclid: 23 November 2012

Permanent link to this document
https://projecteuclid.org/euclid.ajm/1353696018

Mathematical Reviews number (MathSciNet)
MR2989231

Zentralblatt MATH identifier
1266.53065

Subjects
Primary: 53D05: Symplectic manifolds, general 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 58F06

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

Citation

Di Scala, Antonio Jose; Ishi, Hideyuki; Loi, Andrea. Kähler Immersions of Homogeneous Kähler Manifolds into Complex Space Forms. Asian J. Math. 16 (2012), no. 3, 479--488. https://projecteuclid.org/euclid.ajm/1353696018


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