CR Submanifolds of Complex Projective Space

1. Front Matter

   Pages i-viii

   PDF

2. Complex manifolds

   • Mirjana Djorić, Masafumi Okumura

   Pages 1-6

3. Almost complex structure

   • Mirjana Djorić, Masafumi Okumura

   Pages 7-11

4. Complex vector spaces, complexification

   • Mirjana Djorić, Masafumi Okumura

   Pages 13-19

5. Kähler manifolds

   • Mirjana Djorić, Masafumi Okumura

   Pages 21-26

6. Structure equations of a submanifold

   • Mirjana Djorić, Masafumi Okumura

   Pages 27-37

7. Submanifolds of a Euclidean space

   • Mirjana Djorić, Masafumi Okumura

   Pages 39-40

8. Submanifolds of a complex manifold

   • Mirjana Djorić, Masafumi Okumura

   Pages 41-52

9. The Levi form

   • Mirjana Djorić, Masafumi Okumura

   Pages 53-56

10. The principal circle bundle S2n+1(Pn(C), S1)

    • Mirjana Djorić, Masafumi Okumura

    Pages 57-63

11. Submersion and immersion

    • Mirjana Djorić, Masafumi Okumura

    Pages 65-68

12. Hypersurfaces of a Riemannian manifold of constant curvature

    • Mirjana Djorić, Masafumi Okumura

    Pages 69-75

13. Hypersurfaces of a sphere

    • Mirjana Djorić, Masafumi Okumura

    Pages 77-81

14. Hypersurfaces of a sphere with parallel shape operator

    • Mirjana Djorić, Masafumi Okumura

    Pages 83-87

15. Codimension reduction of a submanifold

    • Mirjana Djorić, Masafumi Okumura

    Pages 89-94

16. CR submanifolds of maximal CR dimension

    • Mirjana Djorić, Masafumi Okumura

    Pages 95-101

17. Real hypersurfaces of a complex projective space

    • Mirjana Djorić, Masafumi Okumura

    Pages 103-111

18. Tubes over submanifolds

    • Mirjana Djorić, Masafumi Okumura

    Pages 113-118

19. Levi form of CR submanifolds of maximal CR dimension of a complex space form

    • Mirjana Djorić, Masafumi Okumura

    Pages 119-122

20. Eigenvalues of the shape operator A of CR submanifolds of maximal CR dimension of a complex space form

    • Mirjana Djorić, Masafumi Okumura

    Pages 123-132

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.

• CR Submanifolds
• Complex Manifolds
• Complex Projective Space
• Contact Manifolds
• Djoric
• Kähler manifold
• Levi form
• Mirjana
• Riemannian Manifolds
• Riemannian geometry
• Riemannian manifold
• curvature
• differential geometry
• manifold

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)

• Faculty of Mathematics, University of Belgrade, Belgrade, Serbia

  Mirjana Djoric

• Department of Mathematics, Saitama University, Saitama, Japan

  Masafumi Okumura

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.

Policies and ethics