Riemann geometry without indices

Vladimir V. Fock (1) , Pierre Goussard

1 IRMA - Institut de Recherche Mathématique Avancée

We suggest an index-free formalism allowing to simplify many computations in Riemann geometry. The main ingredients are forms with values in a Clifford algebra and an action of the group $\mathfrak{sl}_2\times \mathfrak{sl}_2$ on such forms.

Domaines: Physique mathématique [math-ph]

Vladimir V. Fock, Pierre Goussard. Riemann geometry without indices. 2018. ⟨hal-01897226⟩