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Lecture Notes of the Unione Matematica Italiana

Kähler Immersions of Kähler Manifolds into Complex Space Forms

Authors: Loi, Andrea, Zedda, Michela

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  • Winner of the 2017 Book Prize of the Unione Matematica Italiana
  • Covers topics not surveyed before in the literature
  • Requires only basic knowledge of complex and Kähler geometry
  • Exercises at the end of each chapter
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About this book

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.

 

Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook $39.99
price for USA in USD
  • ISBN 978-3-319-99483-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA in USD
  • ISBN 978-3-319-99482-6
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually ready to be dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Kähler Immersions of Kähler Manifolds into Complex Space Forms
Authors
Series Title
Lecture Notes of the Unione Matematica Italiana
Series Volume
23
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-319-99483-3
DOI
10.1007/978-3-319-99483-3
Softcover ISBN
978-3-319-99482-6
Series ISSN
1862-9113
Edition Number
1
Number of Pages
X, 100
Number of Illustrations
6 b/w illustrations
Topics

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