Mirjana Djoric, Masafumi Okumura

CR Submanifolds of Complex Projective Space (eBook, PDF)

• Format: PDF

Produktbeschreibung

Althoughsubmanifoldscomplexmanifoldshasbeenanactive?eldofstudyfor many years, in some sense this area is not su?ciently covered in the current literature. This text deals with the CR submanifolds of complex manifolds, with particular emphasis on CR submanifolds of complex projective space, and it covers the topics which are necessary for learning the basic properties of these manifolds. We are aware that it is impossible to give a complete overview of these submanifolds, but we hope that these notes can serve as an introduction to their study. We present the fundamental de?nitions and results necessary for reaching the frontiers of research in this ?eld. There are many monographs dealing with some current interesting topics in di?erential geometry, but most of these are written as encyclopedias, or research monographs, gathering recent results and giving the readers ample usefulinformationaboutthetopics. Therefore, thesekindsofmonographsare attractive to specialists in di?erential geometry and related ?elds and acce- able to professional di?erential geometers. However, for graduate students who are less advanced in di?erential geometry, these texts might be hard to read without assistance from their instructors. By contrast, the general philosophy of this book is to begin with the elementary facts about complex manifolds and their submanifolds, give some details and proofs, and introduce the reader to the study of CR submanifolds of complex manifolds; especially complex projective space. It includes only a few original results with precise proofs, while the others are cited in the reference list.

Produktdetails

• Verlag: Springer New York
• 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.

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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)