This body of work introduces exterior calculus in Euclidean spaces and subsequently implements classical results from standard Riemannian geometry to analyze certain differential forms on a manifold of reference, which here is a symmetric ellipsoid in R n . We focus on the foundations of the theory of differential forms in a progressive approach to present the relevant classical theorems of Green and Stokes and establish volume (length, area or volume) formulas. Furthermore, we introduce the notion of geodesics and show how to obtain them with respect to the reference manifold.
Opara, U (2021). Differential Forms and Applications. Afribary. Retrieved from https://afribary.com/works/differential-forms-and-applications
Opara, Uchechukwu "Differential Forms and Applications" Afribary. Afribary, 16 Apr. 2021, https://afribary.com/works/differential-forms-and-applications. Accessed 16 Nov. 2024.
Opara, Uchechukwu . "Differential Forms and Applications". Afribary, Afribary, 16 Apr. 2021. Web. 16 Nov. 2024. < https://afribary.com/works/differential-forms-and-applications >.
Opara, Uchechukwu . "Differential Forms and Applications" Afribary (2021). Accessed November 16, 2024. https://afribary.com/works/differential-forms-and-applications