Is there a detailed treatment of differential geometry using Robinson's infinitesimals?

I'm not aware of much. But two works worth noting are: K.G. Schlesinger. Generalized Manifolds. Chapman & Hall/CRC, 1997. I.O. Hamad. Generalized curvature and torsion in nonstandard analysis. PhD thesis, Salahaddin University  Erbil, 2007. 


Somewhat belatedly we developed foundations for differential geometry using infinitesimal displacements here: Nowik, T.; Katz, M. "Differential geometry via infinitesimal displacements." Journal of Logic and Analysis 7:5 (2015), 144. 

