Developments in Mathematics

By: Mirjana Djoric, Masafumi Okumura

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Hardcover | 28 October 2009

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Hardcover
186 Pages

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23.5 x 15.88 x 1.91

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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.

Industry Reviews

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)

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