Mirjana Djoric, Masafumi Okumura

CR Submanifolds of Complex Projective Space (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book covers the necessary topics for learning the basic properties of complex manifolds and their submanifolds, offering an easy, friendly, and accessible introduction into the subject while aptly guiding the reader to topics of current research and to more advanced publications.

The book begins with an introduction to the geometry of complex manifolds and their submanifolds and describes the properties of hypersurfaces and CR submanifolds, with particular emphasis on CR submanifolds of maximal CR dimension. The second part contains results which are not new, but recently published in some mathematical journals. The final part contains several original results by the authors, with complete proofs.

Key features of "CR Submanifolds of Complex Projective Space":

- Presents recent developments and results in the study of submanifolds previously published only in research papers.

- Special topics explored include: the Kähler manifold, submersion and immersion, codimension reduction of a submanifold, tubes over submanifolds, geometry of hypersurfaces and CR submanifolds of maximal CR dimension.

- Provides relevant techniques, results and their applications, and presents insight into the motivations and ideas behind the theory.

- Presents the fundamental definitions and results necessary for reaching the frontiers of research in this field.

This text is largely self-contained. Prerequisites include basic knowledge of introductory manifold theory and of curvature properties of Riemannian geometry. Advanced undergraduates, graduate students and researchers in differential geometry will benefit from this concise approach to an important topic.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 176
• Erscheinungstermin: 9. Oktober 2009
• Englisch
• ISBN-13: 9781441904348
• Artikelnr.: 37341715

Autorenporträt

Mirjana Djoric and Masafumi Okumura are widely published in the field of differential geometry. They have each contributed chapters Springer publictations and have co-published 5 papers on the topic of CR submanifolds in Springer Journals.

Inhaltsangabe

Complex manifolds.- Almost complex structure.- Complex vector spaces, complexification.- K#x00E4;hler manifolds.- Structure equations of a submanifold.- Submanifolds of a Euclidean space.- Submanifolds of a complex manifold.- The Levi form.- The principal circle bundle S(P(C), S).- Submersion and immersion.- Hypersurfaces of a Riemannian manifold of constant curvature.- Hypersurfaces of a sphere.- Hypersurfaces of a sphere with parallel shape operator.- Codimension reduction of a submanifold.- CR submanifolds of maximal CR dimension.- Real hypersurfaces of a complex projective space.- Tubes over submanifolds.- Levi form of CR submanifolds of maximal CR dimension of a complex space form.- Eigenvalues of the shape operator of CR submanifolds of maximal CR dimension of a complex space form.- CR submanifolds of maximal CR dimension satisfying the condition (, ) + (, ) = 0.- Contact CR submanifolds of maximal CR dimension.- Invariant submanifolds of real hypersurfaces of complex space forms.- The scalar curvature of CR submanifolds of maximal CR dimension.

Rezensionen

From the reviews: "This book contains a thorough treatment of a particular class of submanifolds, namely CR submanifolds. ... This well written monograph is aimed at researchers who are interested in geometry of complex manifolds and their submanifolds and at graduate students majoring in differential geometry. The material is to a large extent self contained ... . The authors explain in detail techniques which are relevant for this subject and provide motivation for many problems discussed in the book." (Jurgen Berndt, Mathematical Reviews, Issue 2010 h)