Harmonic Vector Fields

Variational Principles and Differential Geometry


  • Sorin Dragomir, University of Basilicata, Potenza, Italy
  • Domenico Perrone, Universita' del Salento, Lecce, Italy

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.
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Computer & Physical Scientists, Engineers, Applied Mathematicians, Structural Geologists


Book information

  • Published: October 2011
  • Imprint: ELSEVIER
  • ISBN: 978-0-12-415826-9


"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

Table of Contents

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