Vector Fields, Differential Forms, and Derivatives

  • Andrei LuduEmail author
Part of the Springer Series in Synergetics book series (SSSYN)


The following results and some of the proofs, can be found in many excellent text books of differential geometry. For example [46] is a very readable and clear textbook with content based on theorems and proofs for geometrical objects in \({\mathbb{R}}^{2,3}\). Shifrin is also an excellent compact and short text rich in applications. For more abstract treatment (I was always puzzled by a book on geometry without any figures) especially on higher than three dimension differentiable manifolds we recommend the classic [158]. At the same level of abstraction, but more focused on specific topics we recommend [306] especially for applications on fiber bundles, [74] for applications concerning vector fields, and [119] for applications towards Lie groups and transformations. In between these levels of approach we also recommend for their wide range of action [19] for a very friendly general treatment of surfaces, or [162] as a very pictorial book on geometry with many applications.


Vector Field Vector Bundle Covariant Derivative Fiber Bundle Integral Curve 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of MathematicsEmbry-Riddle Aeronautical UniversityDaytona BeachUSA

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