Transformation Groups, Exterior Differentiation and Integration

  • Antonio RomanoEmail author
  • Mario Mango Furnari


In this chapter, the one-parameter transformation groups and Lie derivative are defined. Furthermore, two fundamental topics of differential geometry are presented in introductory form: exterior derivative and integration of r-forms. The exterior derivative extends to r-forms the elementary definitions of gradient of a function, curl, and divergence of a vector field as well as the meaning of exact and closed 1-forms. The integration of r-forms allows one to extend the definitions of surface and volume integrals as well as the theorems of Gauss and Stokes.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”Università degli Studi di Napoli Federico IINaplesItaly
  2. 2.Istituto di CiberneticaNaplesItaly

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