Overview
- 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
Part of the book series: Lecture Notes of the Unione Matematica Italiana (UMILN, volume 23)
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Table of contents (7 chapters)
Keywords
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.
Authors and Affiliations
Bibliographic Information
Book Title: Kähler Immersions of Kähler Manifolds into Complex Space Forms
Authors: Andrea Loi, Michela Zedda
Series Title: Lecture Notes of the Unione Matematica Italiana
DOI: https://doi.org/10.1007/978-3-319-99483-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-319-99482-6Published: 11 October 2018
eBook ISBN: 978-3-319-99483-3Published: 20 September 2018
Series ISSN: 1862-9113
Series E-ISSN: 1862-9121
Edition Number: 1
Number of Pages: X, 100
Number of Illustrations: 6 b/w illustrations
Topics: Differential Geometry, Several Complex Variables and Analytic Spaces