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.

This book covers the necessary topics for learning the basic properties of complex manifolds, 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 first half of the book provides an introduction to complex differential geometry and the properties of complex manifolds. The second half describes the properties of hypersurfaces of various complex spaces and CR submanifolds, with particular emphasis on CR submanifolds of maximal CR dimension.

Key features of CR Submanifolds of Complex Projective Space:

-Presents many recent developments and results in the study of CR submanifolds not previously published.

-Special topics explored include: the Kähler manifold, submersion and immersion, and the structure equations of a submanifold.

-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 slim 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.