Kähler Immersions of Kähler Manifolds into Complex Space Forms

Andrea Loi, Michela Zedda (Autoren)

Buch | Softcover

X, 100 Seiten

2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-99482-6 (ISBN)

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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.

- The Diastasis Function.- Calabi's Criterion.- Homogeneous Kähler manifolds.- Kähler-Einstein Manifolds.- Hartogs Type Domains.- Relatives.- Further Examples and Open Problems.

Erscheinungsdatum	13.10.2018
Reihe/Serie	Lecture Notes of the Unione Matematica Italiana
Zusatzinfo	X, 100 p. 6 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	183 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	32Q15, 32A10. • Complex space forms • Homogeneous metrics • KÃ¤hler-Einstein metrics • KÃ¤hler immersions • KÃ¤hler metrics • Kähler-Einstein metrics • Kähler immersions • Kähler metrics
ISBN-10	3-319-99482-4 / 3319994824
ISBN-13	978-3-319-99482-6 / 9783319994826
Zustand	Neuware