Harmonic vector fields : variational principles and differential geometry

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Harmonic vector fields : variational principles and differential geometry / Sorin Dragomir, Domenico Perrone

資料種別:

図書

出版情報:

Amsterdam : Elsevier, c2012

形態:

xiv, 508 p. ; 24 cm

著者名:

ISBN:

9780124158269 [0124158269]

書誌ID:

BB07470626

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

Geometry, Differential; Vector fields

言語:

英語

目次情報:

Preface

Geometry of the Tangent Bundle / 1：

The Tangent Bundle / 1.1：

Connections and Horizontal Vector Fields / 1.2：

The Dombrowski Map and the Sasaki Metric / 1.3：

The Tangent Sphere Bundle / 1.4：

The Tangent Sphere Bundle over a Torus / 1.5：

Harmonic Vector Fields / 2：

Vector Fields as Isometric Immersions / 2.1：

The Energy of a Vector Field / 2.2：

Vector Fields Which Are Harmonic Maps / 2.3：

The Tension of a Vector Field / 2.4：

Variations through Vector Fields / 2.5：

Unit Vector Fields / 2.6：

The Second Variation of the Energy Function / 2.7：

Unboundedness of the Energy Functional / 2.8：

The Dirichlet Problem / 2.9：

Conformal Change of Metric on the Torus / 2.10：

Sobolev Spaces of Vector Fields / 2.11：

Harmonicity and Stability / 3：

Hopf Vector Fields on Spheres / 3.1：

The Energy of Unit Killing Fields in Dimension 3 / 3.2：

instability of Hopf Vector Fields / 3.3：

Existence of Minima in Dimension > 3 / 3.4：

Brito's Functional / 3.5：

The Brito Energy of the Reeb Vector / 3.6：

Vector Fields with Singularities / 3.7：

Normal Vector Fields on Principal Orbits / 3.8：

RiemannianTori / 3.9：

Harmonicity and Contact Metric Structures / 4：

H-Contact Manifolds / 4.1：

Three-Dimensional H-Contact Manifolds / 4.2：

Stability of the Reeb Vector Field / 4.3：

Harmonic Almost Contact Structures / 4.4：

Reeb Vector Fields on Real Hypersurfaces / 4.5：

Harmonicity and Stability of the Geodesic Flow / 4.6：

Harmonicity with Respect to g-Natural Metrics / 5：

g-Natural Metrics / 5.1：

Naturally Harmonic Vector Fields / 5.2：

Vector Fields Which Are Naturally Harmonic Maps / 5.3：

Geodesic Flow with Respect to g-Natural Metrics / 5.4：

The Energy of Sections / 6：

The Horizontal Bundle / 6.1：

The Sasaki Metric / 6.2：

The Sphere Bundle U(E) / 6.3：

The Energy of Cross Sections / 6.4：

Unit Sections / 6.5：

Harmonic Sections in Normal Bundles / 6.6：

The Energy of Oriented Distributions / 6.7：

Examples of Harmonic Distributions / 6.8：

The Chacon-Naveira Energy / 6.9：

Harmonic Vector Fields in CR Geometry / 7：

The Canonical Metric / 7.1：

Bundles of Hyperquadrics in (T(M),J, G_s) / 7.2：

Harmonic Vector Fields from C(M) / 7.3：

Boundary Values of Bergman-Harmonic Maps / 7.4：

Pseudo harmonic Maps / 7.5：

The Pseudo hermitian Biegung / 7.6：

The Second Variation Formula / 7.7：

Lorentz Geometry and Harmonic Vector Fields / 8：

A Few Notions of Lorentz Geometry / 8.1：

Energy Functionals and Tension Fields / 8.2：

The Spacelike Energy / 8.3：

The Second Variation of the Spacelike Energy / 8.4：

Conformal Vector Fields / 8.5：

Twisted Cohomologies / Appendix A：

The Stokes Theorem on Complete Manifolds / Appendix B：

Complex Monge-Ampere Equations / Appendix C：

Introduction / C.1：

Strictly Parabolic Manifolds / C.2：

Foliations and Monge-Ampere Equations / C.3：

Adapted Complex Structures / C.4：

CR Submanifolds of Grauert Tubes / C.5：

Exceptional Orbits of Highest Dimension / Appendix D：

Reilly's Formula / Appendix E：

References

Index

Preface

Geometry of the Tangent Bundle / 1：

The Tangent Bundle / 1.1：

Connections and Horizontal Vector Fields / 1.2：

The Dombrowski Map and the Sasaki Metric / 1.3：

The Tangent Sphere Bundle / 1.4：

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