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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 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.

Mathematics. --- Differential Geometry. --- Global Analysis and Analysis on Manifolds. --- Several Complex Variables and Analytic Spaces. --- Global analysis. --- Differential equations, partial. --- Global differential geometry. --- Mathématiques --- Géométrie différentielle globale --- CR submanifolds. --- Cauchy-Riemann submanifolds --- Submanifolds, CR --- Manifolds (Mathematics) --- Cauchy-Riemann equations. --- Functions of several complex variables. --- CR submanifolds --- Mathematics --- Geometry --- Physical Sciences & Mathematics --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Functions of complex variables. --- Differential geometry. --- Topology. --- Geometry, Differential --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Partial differential equations --- Differential geometry --- Complex variables --- Elliptic functions --- Functions of real variables --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic