Lie Groups II: Differential-Geometric Properties

  • Gregory S. Chirikjian
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)


This chapter discusses how a natural extension of the concept of directional derivatives in Rn can be defined for functions on Lie groups. This “Lie derivative” is closely related to the differential geometric properties of the group. Functions on a Lie group can be expanded in a Taylor series using Lie derivatives. Explicit expressions for these Lie derivatives in a particular parametrization can be easily obtained for Lie groups using the appropriate concept of a Jacobian matrix as defined in the previous chapter.


Taylor Series Chain Rule Jacobian Matrice Real Analytic Function Exterior Derivative 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe Johns Hopkins UniversityBaltimoreUSA

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