Ebook: CR Submanifolds of Complex Projective Space

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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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 K?hler 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.

---

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 K?hler 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.

Content:
Front Matter....Pages i-viii
Complex manifolds....Pages 1-6
Almost complex structure....Pages 7-11
Complex vector spaces, complexification....Pages 13-19
K?hler manifolds....Pages 21-26
Structure equations of a submanifold....Pages 27-37
Submanifolds of a Euclidean space....Pages 39-40
Submanifolds of a complex manifold....Pages 41-52
The Levi form....Pages 53-56
The principal circle bundle S2n+1(Pn(C), S1)....Pages 57-63
Submersion and immersion....Pages 65-68
Hypersurfaces of a Riemannian manifold of constant curvature....Pages 69-75
Hypersurfaces of a sphere....Pages 77-81
Hypersurfaces of a sphere with parallel shape operator....Pages 83-87
Codimension reduction of a submanifold....Pages 89-94
CR submanifolds of maximal CR dimension....Pages 95-101
Real hypersurfaces of a complex projective space....Pages 103-111
Tubes over submanifolds....Pages 113-118
Levi form of CR submanifolds of maximal CR dimension of a complex space form....Pages 119-122
Eigenvalues of the shape operator A of CR submanifolds of maximal CR dimension of a complex space form....Pages 123-132
CR submanifolds of maximal CR dimension satisfying the condition h(FX, Y) + h(X, FY) = 0....Pages 133-137
Contact CR submanifolds of maximal CR dimension....Pages 139-149
Invariant submanifolds of real hypersurfaces of complex space forms....Pages 151-161
The scalar curvature of CR submanifolds of maximal CR dimension....Pages 163-167
Back Matter....Pages 1-7

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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 K?hler 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.

Content:
Front Matter....Pages i-viii
Complex manifolds....Pages 1-6
Almost complex structure....Pages 7-11
Complex vector spaces, complexification....Pages 13-19
K?hler manifolds....Pages 21-26
Structure equations of a submanifold....Pages 27-37
Submanifolds of a Euclidean space....Pages 39-40
Submanifolds of a complex manifold....Pages 41-52
The Levi form....Pages 53-56
The principal circle bundle S2n+1(Pn(C), S1)....Pages 57-63
Submersion and immersion....Pages 65-68
Hypersurfaces of a Riemannian manifold of constant curvature....Pages 69-75
Hypersurfaces of a sphere....Pages 77-81
Hypersurfaces of a sphere with parallel shape operator....Pages 83-87
Codimension reduction of a submanifold....Pages 89-94
CR submanifolds of maximal CR dimension....Pages 95-101
Real hypersurfaces of a complex projective space....Pages 103-111
Tubes over submanifolds....Pages 113-118
Levi form of CR submanifolds of maximal CR dimension of a complex space form....Pages 119-122
Eigenvalues of the shape operator A of CR submanifolds of maximal CR dimension of a complex space form....Pages 123-132
CR submanifolds of maximal CR dimension satisfying the condition h(FX, Y) + h(X, FY) = 0....Pages 133-137
Contact CR submanifolds of maximal CR dimension....Pages 139-149
Invariant submanifolds of real hypersurfaces of complex space forms....Pages 151-161
The scalar curvature of CR submanifolds of maximal CR dimension....Pages 163-167
Back Matter....Pages 1-7
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