Harmonic Vector Fields book cover

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.


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

Hardbound, 528 Pages

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


  • 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


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