La théorie des repères mobiles et des formes différentielles quadratiques en espaces banachiques (Q788353)

In this paper, a Banach space version of Elie Cartan's moving frame method is developed. Geometric objects are defined by parametrizations, and the existence of corresponding moving frames is proven. The developed formalism is then used to study suitably defined hypersurfaces in Banach spaces, and to prove generalizations of the Gauss and Mainardi-Codazzi integrability conditions, and of the Bonnet existence theorem.