Transformation Groups, Exterior Differentiation and Integration

Antonio Romano () and Mario Mango Furnari ()
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Antonio Romano: Università degli Studi di Napoli Federico II, Dipartimento di Matematica e Applicazioni “Renato Caccioppoli”
Mario Mango Furnari: Consiglio Nazionale delle Ricerche, Istituto di Cibernetica

Chapter 3 in The Physical and Mathematical Foundations of the Theory of Relativity, 2026, pp 105-129 from Springer

Abstract: Abstract 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.

Date: 2026
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DOI: 10.1007/978-3-032-23179-6_3

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