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Cartan geometry is the geometry of spaces that are locally (infinitesimally, tangentially) like coset spaces G/H, i.e. like Klein geometries. Intuitively, Cartan geometry studies the geometry of a manifold by ‘rolling without sliding’ the ‘model geometry’ G/H along it. Hence Cartan geometry may be thought of as the globalization of the program of Klein geometry initiated in the Erlangen program.
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Restriction of complete 1-forms to closed submanifolds (Sharpe's book on Cartan geometries)
In his Book Differential Geometry: Cartan's generalization of Klein's Erlangen Program, Sharpe gives the following definition of a complete 1-form:
Soon thereafter he gives the following example:
I …