Harmonic Vector Fields: Variational Principles and Differential Geometry

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 analysisProvides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifoldsPhysical Applications of Geometric Methods

Chapter 1: Geometry of Tangent Bundle Chapter 2: Harmonic Vector Fields Chapter 3: Harmonicity and Stability Chapter 4: Harmonicity and Contact Metric Structures Chapter 5: Harmonicity with Respect to G-Natural Metrics Chapter 6: The Energy of Sections Chapter 7: Harmonic Vector Fields in CR Geometry Chapter 8: Lorentz Geometry and Harmonic Vector Fields Appendix A: Twisted Cohomologies Appendix B: The Stokes Theorem on Complete Manifolds Appendix C: Complex Monge-Ampere Equations Appendix D: Exceptional Orbits of Highest Dimension Appendix E: Reilly’s Formula Bibliography Index