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Harmonic Vector Fields: Variational Principles and Differential Geometry [Kõva köide]

(University of Basilicata, Potenza, Italy), (Universita' del Salento, Lecce, Italy)
  • Formaat: Hardback, 528 pages, kõrgus x laius: 229x152 mm, kaal: 830 g
  • Ilmumisaeg: 06-Dec-2011
  • Kirjastus: Elsevier Science Publishing Co Inc
  • ISBN-10: 0124158269
  • ISBN-13: 9780124158269
Teised raamatud teemal:
Harmonic Vector Fields: Variational Principles and Differential GeometrySuurem pilt
  • Formaat: Hardback, 528 pages, kõrgus x laius: 229x152 mm, kaal: 830 g
  • Ilmumisaeg: 06-Dec-2011
  • Kirjastus: Elsevier Science Publishing Co Inc
  • ISBN-10: 0124158269
  • ISBN-13: 9780124158269
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780124158269.html
Märksõnad:

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector fields with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail.


  • A useful tool for any scientist conducting research in the field of harmonic analysis

  • Provides applications and modern techniques to problem solving

  • A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds

  • Physical Applications of Geometric Methods

Arvustused

"This monograph (over 500 pages) is well written and self-contained in the field of harmonic vector fields..."--Mathematical Reviews, Harmonic Vector Fields

"The book is certainly a valuable reference sourceThe bibliography appears both extensive and carefully selected...The style of formal statements is clear and helpful when browsing for specific results."--Zentralblatt MATH 2012-1245-53002

Muu info

An essential reference for any scientist conducting research in the rapidly developing area of harmonic analysis
Preface ix
1 Geometry of the Tangent Bundle
1(36)
1.1 The Tangent Bundle
2(2)
1.2 Connections and Horizontal Vector Fields
4(2)
1.3 The Dombrowski Map and the Sasaki Metric
6(20)
1.4 The Tangent Sphere Bundle
26(3)
1.5 The Tangent Sphere Bundle over a Torus
29(8)
2 Harmonic Vector Fields
37(92)
2.1 Vector Fields as Isometric Immersions
38(3)
2.2 The Energy of a Vector Field
41(5)
2.3 Vector Fields Which Are Harmonic Maps
46(3)
2.4 The Tension of a Vector Field
49(7)
2.5 Variations through Vector Fields
56(2)
2.6 Unit Vector Fields
58(15)
2.7 The Second Variation of the Energy Function
73(8)
2.8 Unboundedness of the Energy Functional
81(1)
2.9 The Dirichlet Problem
82(24)
2.10 Conformal Change of Metric on the Torus
106(2)
2.11 Sobolev Spaces of Vector Fields
108(21)
3 Harmonicity and Stability
129(76)
3.1 Hopf Vector Fields on Spheres
30(110)
3.2 The Energy of Unit Killing Fields in Dimension 3
140(6)
3.3 Instability of Hopf Vector Fields
146(5)
3.4 Existence of Minima in Dimension > 3
151(4)
3.5 Brito's Functional
155(3)
3.6 The Brito Energy of the Reeb Vector
158(6)
3.7 Vector Fields with Singularities
164(15)
3.8 Normal Vector Fields on Principal Orbits
179(9)
3.9 Riemannian Tori
188(17)
4 Harmonicity and Contact Metric Structures
205(68)
4.1 H-Contact Manifolds
206(12)
4.2 Three-Dimensional H-Contact Manifolds
218(15)
4.3 Stability of the Reeb Vector Field
233(10)
4.4 Harmonic Almost Contact Structures
243(2)
4.5 Reeb Vector Fields on Real Hypersurfaces
245(14)
4.6 Harmonicity and Stability of the Geodesic Flow
259(14)
5 Harmonicity with Respect to g-Natural Metrics
273(34)
5.1 g-Natural Metrics
275(7)
5.2 Naturally Harmonic Vector Fields
282(8)
5.3 Vector Fields Which Are Naturally Harmonic Maps
290(12)
5.4 Geodesic Flow with Respect to g-Natural Metrics
302(5)
6 The Energy of Sections
307(48)
6.1 The Horizontal Bundle
309(7)
6.2 The Sasaki Metric
316(4)
6.3 The Sphere Bundle U(E)
320(4)
6.4 The Energy of Cross Sections
324(2)
6.5 Unit Sections
326(3)
6.6 Harmonic Sections in Normal Bundles
329(3)
6.7 The Energy of Oriented Distributions
332(5)
6.8 Examples of Harmonic Distributions
337(7)
6.9 The Chacon-Naveira Energy
344(11)
7 Harmonic Vector Fields in CR Geometry
355(52)
7.1 The Canonical Metric
359(6)
7.2 Bundles of Hyperquadrics in (T(M), J, Gs)
365(12)
7.3 Harmonic Vector Fields from C(M)
377(10)
7.4 Boundary Values of Bergman-Harmonic Maps
387(2)
7.5 Pseudoharmonic Maps
389(5)
7.6 The Pseudohermitian Biegung
394(7)
7.7 The Second Variation Formula
401(6)
8 Lorentz Geometry and Harmonic Vector Fields
407(30)
8.1 A Few Notions of Lorentz Geometry
407(3)
8.2 Energy Functionals and Tension Fields
410(2)
8.3 The Spacelike Energy
412(19)
8.4 The Second Variation of the Spacelike Energy
431(3)
8.5 Conformal Vector Fields
434(3)
Appendix A Twisted Cohomologies
437(10)
Appendix B The Stokes Theorem on Complete Manifolds
447(10)
Appendix C Complex Monge-Ampere Equations
457(16)
C.1 Introduction
457(3)
C.2 Strictly Parabolic Manifolds
460(1)
C.3 Foliations and Monge-Ampere Equations
461(3)
C.4 Adapted Complex Structures
464(4)
C.5 CRc Submanifolds of Grauert Tubes
468(5)
Appendix D Exceptional Orbits of Highest Dimension
473(6)
Appendix E Reilly's Formula
479(12)
References 491(14)
Index 505