Harmonic Vector Fields: Variational Principles and Differential Geometry

ISBN-13: 9780124158269 / Angielski / Twarda / 2011 / 508 str.

Sorin Dragomir; Domenico Perrone

Opis

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

Recenzje

"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 source.The 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

Spis treści

Chapter 1: Geometry of Tangent BundleChapter 2: Harmonic Vector FieldsChapter 3: Harmonicity and Stability Chapter 4: Harmonicity and Contact Metric StructuresChapter 5: Harmonicity with Respect to G-Natural MetricsChapter 6: The Energy of SectionsChapter 7: Harmonic Vector Fields in CR GeometryChapter 8: Lorentz Geometry and Harmonic Vector FieldsAppendix A: Twisted CohomologiesAppendix B: The Stokes Theorem on Complete ManifoldsAppendix C: Complex Monge-Ampere EquationsAppendix D: Exceptional Orbits of Highest DimensionAppendix E: Reilly's FormulaBibliographyIndex