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Kähler immersions of Kähler manifolds into complex space forms

Author: Andrea Loi; Michela Zedda
Publisher: Cham, Switzerland : Springer, [2018] ©2018
Series: Lecture notes of the Unione Matematica Italiana, 23.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
The aim of this book is to describe Calabi's original work on Kähler immersions of Kähler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and to point out some open problems. Calabi's pioneering work, making use of the powerful tool of the diastasis function, allowed him to obtain necessary and sufficient conditions for a neighbourhood of a point to be locally  Read more...
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Genre/Form: Electronic books
Additional Physical Format: (OCoLC)1045494093
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Andrea Loi; Michela Zedda
ISBN: 9783319994833 3319994832 9783319994840 3319994840
OCLC Number: 1054092794
Description: 1 online resource.
Contents: Intro; Preface; Contents; 1 The Diastasis Function; 1.1 Calabi's Diastasis Function; 1.2 Complex Space Forms; 1.3 The Indefinite Hilbert Space; Exercises; 2 Calabi's Criterion; 2.1 Kähler Immersions into the Complex Euclidean Space; 2.2 Kähler Immersions into Nonflat Complex Space Forms; 2.3 Kähler Immersions of a Complex Space Form into Another; Exercises; 3 Homogeneous Kähler Manifolds; 3.1 A Result About Kähler Immersions of Homogeneous Bounded Domains into CP∞; 3.2 Kähler Immersions of Homogeneous Kähler Manifolds into CN≤∞ and CHN≤∞ 3.3 Kähler Immersions of Homogeneous Kähler Manifolds into CPN≤∞3.4 Bergman Metric and Bounded Symmetric Domains; 3.5 Kähler Immersions of Bounded Symmetric Domains into CP∞; Exercises; 4 Kähler-Einstein Manifolds; 4.1 Kähler Immersions of Kähler-Einstein Manifoldsinto CHN or CN; 4.2 Kähler Immersions of KE Manifolds into CPN: The Einstein Constant; 4.3 Kähler Immersions of KE Manifolds into CPN: Codimension 1 and 2; Exercises; 5 Hartogs Type Domains; 5.1 Cartan-Hartogs Domains; 5.2 Bergman-Hartogs Domains; 5.3 Rotation Invariant Hartogs Domains; Exercises; 6 Relatives 6.1 Relatives Complex Space Forms6.2 Homogeneous Kähler Manifolds Are Not Relative to Projective Ones; 6.3 Bergman-Hartogs Domains Are Not Relative to a Projective Kähler Manifold; Exercises; 7 Further Examples and Open Problems; 7.1 The Cigar Metric on C; 7.2 Calabi's Complete and Not Locally Homogeneous Metric; 7.3 The Taub-NUT Metric on C2; Exercises; References; Index
Series Title: Lecture notes of the Unione Matematica Italiana, 23.
Responsibility: Andrea Loi, Michela Zedda.

Abstract:

The aim of this book is to describe Calabi's original work on Kahler immersions of Kahler manifolds into complex space forms, to provide a detailed account of what is known today on the subject and  Read more...

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