Format:
Online-Ressource
,
v.: digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
1282834959
,
9781441904331
,
9781282834958
Series Statement:
Developments in Mathematics, Diophantine Approximation 19
Content:
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.
Note:
Includes bibliographical references and index
,
CR SUBMANIFOLDSOF COMPLEX PROJECTIVE SPACE; Contents; Preface; Complex manifolds; Almost complex structure; Complex vector spaces, complexification; Kähler manifolds; Structure equations of a submanifold; Submanifolds of a Euclidean space; Submanifolds of a complex manifold; The Levi form; The principal circle bundle S2n+1(Pn(C),S1); Submersion and immersion; Hypersurfaces of a Riemannian manifold of constant curvature; Hypersurfaces of a sphere; Hypersurfaces of a sphere with parallel shape operator; Codimension reduction of a submanifold; CR submanifolds of maximal CR dimension
,
Real hypersurfaces of a complex projective spaceTubes over submanifolds; Levi form of CR submanifolds of maximal CR dimension of a complex space form; Eigenvalues of the shape operator A of CR submanifolds of maximal CR dimension of a complex space form; CR submanifolds of maximal CR dimension satisfying the condition h(FX,Y)+h(X,FY)=0; Contact CR submanifolds of maximal CR dimension; Invariant submanifolds of real hypersurfaces of complex space forms; The scalar curvature of CR submanifolds of maximal CR dimension; References; List of symbols; Subject index
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9781441904348
Additional Edition:
ISBN 9781441904331
Additional Edition:
Erscheint auch als Druck-Ausgabe Djoric, Mirjana CR submanifolds of complex projective space New York, NY : Springer, 2010 ISBN 9781441904331
Language:
English
Subjects:
Mathematics
Keywords:
Cauchy-Riemannsche Mannigfaltigkeit
;
Untermannigfaltigkeit
;
Komplexer projektiver Raum
DOI:
10.1007/978-1-4419-0434-8
URL:
Volltext
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