Kähler immersions of Kähler manifolds into complex space forms /
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| Author / Creator: | Loi, Andrea, author. |
|---|---|
| Imprint: | Cham, Switzerland : Springer, [2018] ©2018 |
| Description: | 1 online resource |
| Language: | English |
| Series: | Lecture notes of the Unione Matematica Italiana ; 23 Lecture notes of the Unione Matematica Italiana ; 23. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11737065 |
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| 100 | 1 | |a Loi, Andrea, |e author. | |
| 245 | 1 | 0 | |a Kähler immersions of Kähler manifolds into complex space forms / |c Andrea Loi, Michela Zedda. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2018] | |
| 264 | 4 | |c ©2018 | |
| 300 | |a 1 online resource | ||
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| 490 | 1 | |a Lecture notes of the Unione Matematica Italiana ; |v 23 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Vendor-supplied metadata. | |
| 505 | 0 | |a 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≤∞ | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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 | |
| 520 | |a 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 Kähler immersed into a finite or infinite-dimensional complex space form. This led to a classification of (finite-dimensional) complex space forms admitting a Kähler immersion into another, and to decades of further research on the subject. Each chapter begins with a brief summary of the topics to be discussed and ends with a list of exercises designed to test the reader's understanding. Apart from the section on Kähler immersions of homogeneous bounded domains into the infinite complex projective space, which could be skipped without compromising the understanding of the rest of the book, the prerequisites to read this book are a basic knowledge of complex and Kähler geometry.-- |c Provided by publisher. | ||
| 650 | 0 | |a Kählerian manifolds. |0 http://id.loc.gov/authorities/subjects/sh85071275 | |
| 650 | 0 | |a Immersions (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85064515 | |
| 650 | 0 | |a Manifolds (Mathematics) |0 http://id.loc.gov/authorities/subjects/sh85080549 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Complex analysis, complex variables. |2 bicssc | |
| 650 | 7 | |a Differential & Riemannian geometry. |2 bicssc | |
| 650 | 7 | |a Immersions (Mathematics) |2 fast |0 (OCoLC)fst00967708 | |
| 650 | 7 | |a Kählerian manifolds. |2 fast |0 (OCoLC)fst00989676 | |
| 650 | 7 | |a Manifolds (Mathematics) |2 fast |0 (OCoLC)fst01007726 | |
| 655 | 4 | |a Electronic books. | |
| 700 | 1 | |a Zedda, Michela, |e author. | |
| 776 | 0 | 8 | |i Print version: |a Loi, Andrea. |t Kähler immersions of Kähler manifolds into complex space forms. |d Cham, Switzerland : Springer, [2018] |z 3319994824 |z 9783319994826 |w (OCoLC)1045494093 |
| 830 | 0 | |a Lecture notes of the Unione Matematica Italiana ; |v 23. |0 http://id.loc.gov/authorities/names/no2006133097 | |
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