CR Submanifolds of Complex Projective Space

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ISBN: 978-1-4419-0433-1 (Print) 978-1-4419-0434-8 (Online)

Table of contents (23 chapters)

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  1. Front Matter

    Pages i-viii

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    Book Chapter

    Pages 1-6

    Complex manifolds

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    Pages 7-11

    Almost complex structure

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    Pages 13-19

    Complex vector spaces, complexification

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    Pages 21-26

    Kähler manifolds

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    Pages 27-37

    Structure equations of a submanifold

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    Pages 39-40

    Submanifolds of a Euclidean space

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    Pages 41-52

    Submanifolds of a complex manifold

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    Pages 53-56

    The Levi form

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    Pages 57-63

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

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    Pages 65-68

    Submersion and immersion

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    Pages 69-75

    Hypersurfaces of a Riemannian manifold of constant curvature

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    Pages 77-81

    Hypersurfaces of a sphere

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    Pages 83-87

    Hypersurfaces of a sphere with parallel shape operator

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    Pages 89-94

    Codimension reduction of a submanifold

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    Pages 95-101

    CR submanifolds of maximal CR dimension

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    Pages 103-111

    Real hypersurfaces of a complex projective space

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    Pages 113-118

    Tubes over submanifolds

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    Pages 119-122

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

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    Pages 123-132

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

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    Book Chapter

    Pages 133-137

    CR submanifolds of maximal CR dimension satisfying the condition h(FX, Y) + h(X, FY) = 0

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